source_dataset stringclasses 1
value | question stringlengths 6 1.87k | choices stringlengths 20 1.02k | answer stringclasses 4
values | rationale float64 | documents stringlengths 1.01k 5.9k |
|---|---|---|---|---|---|
epfl-collab | Graph coloring consist of coloring all vertices \ldots | ['\\ldots with a unique color.', '\\ldots with a random color.', '\\ldots with a maximum number of colors.', '\\ldots with a different color when they are linked with an edge.'] | D | null | Document 1:::
Graph color
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are o... |
epfl-collab | What adversarial model does not make sense for a message authentication code (MAC)? | ['key recovery.', 'existential forgery.', 'decryption.', 'universal forgery.'] | C | null | Document 1:::
Adversarial machine learning
Adversarial machine learning is the study of the attacks on machine learning algorithms, and of the defenses against such attacks. A survey from May 2020 exposes the fact that practitioners report a dire need for better protecting machine learning systems in industrial applica... |
epfl-collab | Which one of these ciphers does achieve perfect secrecy? | ['DES', 'Vernam', 'RSA', 'FOX'] | B | null | Document 1:::
Block cipher
Even a secure block cipher is suitable for the encryption of only a single block of data at a time, using a fixed key. A multitude of modes of operation have been designed to allow their repeated use in a secure way to achieve the security goals of confidentiality and authenticity. However, b... |
epfl-collab | Which of the following problems has not been shown equivalent to the others? | ['The RSA Order Problem.', 'The RSA Factorization Problem.', 'The RSA Key Recovery Problem.', 'The RSA Decryption Problem.'] | D | null | Document 1:::
Nonelementary problem
In computational complexity theory, a nonelementary problem is a problem that is not a member of the class ELEMENTARY. As a class it is sometimes denoted as NONELEMENTARY. Examples of nonelementary problems that are nevertheless decidable include: the problem of regular expression eq... |
epfl-collab | A proof system is perfect-black-box zero-knowledge if \dots | ['for any PPT verifier $V$, there exists a PPT simulator $S$, such that $S$ produces an output which is hard to distinguish from the view of the verifier.', 'for any PPT simulator $S$ and for any PPT verifier $V$, $S^{V}$ produces an output which has the same distribution as the view of the verifier.', 'there exists a ... | D | null | Document 1:::
Zero-knowledge proofs
A zero-knowledge proof of some statement must satisfy three properties: Completeness: if the statement is true, an honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prov... |
epfl-collab | Suppose that you can prove the security of your symmetric encryption scheme against the following attacks. In which case is your scheme going to be the \textbf{most} secure? | ['Key recovery under known plaintext attack.', 'Decryption under known plaintext attack.', 'Key recovery under chosen ciphertext attack.', 'Decryption under chosen ciphertext attack.'] | D | null | Document 1:::
Known-key distinguishing attack
In cryptography, a known-key distinguishing attack is an attack model against symmetric ciphers, whereby an attacker who knows the key can find a structural property in cipher, where the transformation from plaintext to ciphertext is not random. There is no common formal de... |
epfl-collab | For a $n$-bit block cipher with $k$-bit key, given a plaintext-ciphertext pair, a key exhaustive search has an average number of trials of \dots | ['$2^n$', '$2^k$', '$\\frac{2^k+1}{2}$', '$\\frac{2^n+1}{2}$'] | C | null | Document 1:::
Completeness (cryptography)
In cryptography, a boolean function is said to be complete if the value of each output bit depends on all input bits. This is a desirable property to have in an encryption cipher, so that if one bit of the input (plaintext) is changed, every bit of the output (ciphertext) has a... |
epfl-collab | Tick the \textbf{false} assertion. For a Vernam cipher... | ['CRYPTO can be used as a key to encrypt the plaintext PLAIN', 'SERGE can be the ciphertext corresponding to the plaintext VAUDENAY', 'SUPERMAN can be the result of the encryption of the plaintext ENCRYPT', 'The key IAMAKEY can be used to encrypt any message of size up to 7 characters'] | B | null | Document 1:::
Padding oracle attack
In cryptography, a padding oracle attack is an attack which uses the padding validation of a cryptographic message to decrypt the ciphertext. In cryptography, variable-length plaintext messages often have to be padded (expanded) to be compatible with the underlying cryptographic prim... |
epfl-collab | Assume we are in a group $G$ of order $n = p_1^{\alpha_1} p_2^{\alpha_2}$, where $p_1$ and $p_2$ are two distinct primes and $\alpha_1, \alpha_2 \in \mathbb{N}$. The complexity of applying the Pohlig-Hellman algorithm for computing the discrete logarithm in $G$ is \ldots (\emph{choose the most accurate answer}): | ['$\\mathcal{O}( \\alpha_1 \\sqrt{p_1} + \\alpha_2 \\sqrt{p_2})$.', '$\\mathcal{O}(\\alpha_1 p_1^{\\alpha_1 -1} + \\alpha_2 p_2^{\\alpha_2 -1})$.', '$\\mathcal{O}( \\alpha_1 \\log{p_1} + \\alpha_2 \\log{p_2})$.', '$\\mathcal{O}(\\sqrt{p_1}^{\\alpha_1} + \\sqrt{p_2}^{\\alpha_2})$.'] | A | null | Document 1:::
Pohlig–Hellman algorithm
In group theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms in a finite abelian group whose order is a smooth integer. The algorithm was introduced by Roland Silver, but ... |
epfl-collab | Tick the \textbf{\emph{incorrect}} assertion. | ['$PSPACE\\subseteq IP$.', '$NP\\mbox{-hard} \\subset P$.', '$P\\subseteq NP$.', '$NP\\subseteq IP$.'] | B | null | Document 1:::
Talk:Fibonacci sequence
WP:CITEVAR is very clear that you should not be changing citation styles in this way without consensus. For those of us who use User:BrandonXLF/CitationStyleMarker.js to find inconsistent citation styles, your change is very annoying because it causes all of the citations to be fla... |
epfl-collab | Tick the \emph{correct} statement. $\Sigma$-protocols \ldots | ['respect the property of zero-knowledge for any verifier.', 'consist of protocols between a prover and a verifier, where the verifier is polynomially bounded.', 'are defined for any language in \\textrm{PSPACE}.', 'have a polynomially unbounded extractor that can yield a witness.'] | B | null | Document 1:::
Security protocol notation
In cryptography, security (engineering) protocol notation, also known as protocol narrations and Alice & Bob notation, is a way of expressing a protocol of correspondence between entities of a dynamic system, such as a computer network. In the context of a formal model, it allow... |
epfl-collab | Which defense(s) highlight the principle of least privilege in software
security? | ['DEP bits by disallowing execution on certain memory pages because code is restricted to code pages.', 'CFI protection on the forward edge because the check limits reachable targets.', 'A stack canary because it will signal any stack-based attack.', 'Applying updates regularly because software updates always reduce pr... | A | null | Document 1:::
Protected procedure
In computer science, the concept of protected procedure, first introduced as protected service routine in 1965, is necessary when two computations A and B use the same routine S; a protected procedure is such if makes not possible for a malfunction of one of the two computation to caus... |
epfl-collab | For which kind of bugs does default LLVM provide sanitizers? | ['Buffer overflows', 'Race conditions between threads', 'Logic bugs', 'Memory leaks'] | D | null | Document 1:::
Segmentation violation
Processes can in some cases install a custom signal handler, allowing them to recover on their own, but otherwise the OS default signal handler is used, generally causing abnormal termination of the process (a program crash), and sometimes a core dump. Segmentation faults are a comm... |
epfl-collab | Which of the following hold(s) true about update deployment in the secure
development lifecycle? | ['Updates may bring new code that may be buggy, so additional\n monitoring is required after deploying an update.', 'You should always deploy third party updates automatically\n and immediately in your project.', 'One motivation for automatic updates is for manufacturers to\n ensure tha... | A | null | Document 1:::
Slipstream (computing)
Even when the source code is available, patching makes possible the installation of small changes to the object program without the need to recompile or reassemble. For minor changes to software, it is often easier and more economical to distribute patches to users rather than redis... |
epfl-collab | Current software is complex and often relies on external dependencies.
What are the security implications? | ['During the requirement phase of the secure development\n lifecycle, a developer must list all the required dependencies.', 'Closed source code is more secure than open source code as it\n prohibits other people from finding security bugs.', 'As most third party software is open source, it is saf... | A | null | Document 1:::
Software dependency
In computer science, a library is a collection of non-volatile resources used by computer programs, often for software development. These may include configuration data, documentation, help data, message templates, pre-written code and subroutines, classes, values or type specification... |
epfl-collab | Daemons are just long running processes. When applying mitigations to these
processes, several aspects change. Which ones? | ['CFI becomes less effective as the concurrent clients cause\n more targets to be available.', 'Stack canaries become less effective as multiple requests are\n handled by the same thread.', 'DEP becomes less effective as compiler optimizations are\n turned on, allowing the attacker to i... | D | null | Document 1:::
Resource leak
In other cases resource leaks can be a major problem, causing resource starvation and severe system slowdown or instability, crashing the leaking process, other processes, or even the system. Resource leaks often go unnoticed under light load and short runtimes, and these problems only manif... |
epfl-collab | Which of the following apply to recent Android-based mobile systems but not
to Linux-based desktop systems? | ['By default, each app runs as its own user.', 'Arbitrary apps can exchange files through shared\n directories.', 'All apps run in a strict container with only limited system\n calls available.', 'Apps should use the binder interface to communicate with other\n apps.'] | D | null | Document 1:::
KDE Connect
KDE Connect is a multi-platform application developed by KDE, which facilitates wireless communications and data transfer between devices over local networks. KDE Connect is available in the repositories of many Linux Distributions and F-Droid, Google Play Store for Android. Often, distributio... |
epfl-collab | Which of the following attack vectors apply to mobile Android systems? | ['Hardware vendors like \\$am\\$ung are primarily interested in making\n money and not in providing software updates, resulting in outdated\n software that is vulnerable to attacks.', 'Malicious apps can intercept network traffic of benign apps.', 'Apps may maliciously declare intent filters to re... | C | null | Document 1:::
Attack vector
In computer security, an attack vector is a specific path, method, or scenario that can be exploited to break into an IT system, thus compromising its security. The term was derived from the corresponding notion of vector in biology. An attack vector may be exploited manually, automatically,... |
epfl-collab | Does AddressSanitizer prevent \textbf{all} use-after-free bugs? | ['Yes, because free’d memory is unmapped and accesses therefore\n cause segmentation faults.', 'No, because quarantining free’d memory chunks forever prevents\n legit memory reuse and could potentially lead to out-of-memory\n situations.', 'Yes, because free’d memory chunks are poisoned... | B | null | Document 1:::
Heap corruption
Using memory beyond the memory that was allocated (buffer overflow): If an array is used in a loop, with incorrect terminating condition, memory beyond the array bounds may be accidentally manipulated. Buffer overflow is one of the most common programming flaws exploited by computer viruse... |
epfl-collab | For security reasons, you accept the performance and memory overhead
introduced by common sanitizers and deploy them in your user-facing
production server software.
Assuming that all memory safety bugs in your software are detected by the
sanitizers, which of the following properties do the sanitizers p... | ['Accountability of accesses to the program', 'Availability of the program', 'Confidentiality of the program data', 'Integrity of the program data'] | C | null | Document 1:::
Memory protection
Protection may encompass all accesses to a specified area of memory, write accesses, or attempts to execute the contents of the area. An attempt to access unauthorized memory results in a hardware fault, e.g., a segmentation fault, storage violation exception, generally causing abnormal ... |
epfl-collab | What is/are the goal/s of compartmentalization? | ['Make faults more severe as the surrounding code is smaller.', 'Better performance (i.e., lower overhead) since a compartment\n can fail without affecting others.', 'Isolate faults to individual (ideally small) components.', 'Allow easier abstraction of functionalities across components.'] | C | null | Document 1:::
In vitro compartmentalization
In vitro compartmentalization (IVC) is an emulsion-based technology that generates cell-like compartments in vitro. These compartments are designed such that each contains no more than one gene. When the gene is transcribed and/or translated, its products (RNAs and/or protein... |
epfl-collab | Which of the following statements about code instrumentation is/are correct? | ['We should instrument basic blocks when collecting edge coverage.', 'We can only do binary rewriting on position-independent code (PIC).', 'The instrumentation code for coverage collection should not\n change the original functionality.', 'Binary rewriting-based coverage collection has lower runtime\n ... | A | null | Document 1:::
Instrumentation (computer programming)
In the context of computer programming, instrumentation refers to the measure of a product's performance, in order to diagnose errors and to write trace information. Instrumentation can be of two types: source instrumentation and binary instrumentation.
Document 2:::... |
epfl-collab | Which of the following statements about libFuzzer is/are correct? | ['libFuzzer can only test single-threaded targets.', 'It is better to put narrow targets into the fuzzing stubs, e.g.,\n if a target can parse several data formats, split it into several\n targets, one per format.', 'Unit tests may serve as foundation to create libFuzzer fuzzing\n stubs... | C | null | Document 1:::
Lempel–Ziv–Oberhumer
Lempel–Ziv–Oberhumer (LZO) is a lossless data compression algorithm that is focused on decompression speed.
Document 2:::
Lempel–Ziv–Welch
Lempel–Ziv–Welch (LZW) is a universal lossless data compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. It was published ... |
epfl-collab | Which of the following statements about symbolic execution is/are correct? | ['State space explosion is a common challenge for symbolic\n execution.', 'Symbolic execution requires actually running the target\n program.', 'Symbolic execution can efficiently handle and solve constraints\n in programs with simple logics but large input space.', "Symbolic execution ... | C | null | Document 1:::
Symbolic execution
In computer science, symbolic execution (also symbolic evaluation or symbex) is a means of analyzing a program to determine what inputs cause each part of a program to execute. An interpreter follows the program, assuming symbolic values for inputs rather than obtaining actual inputs as... |
epfl-collab | Which of the following statements about coverage-guided fuzzing is/are correct? | ['Redundant seeds in the corpus will reduce fuzzing efficiency.', 'Due to the coverage feedback, a small random perturbation of a\n seed can have a significant impact on further exploration.', 'Counting the number of times the covered code has been executed\n provides a more fine-grained view of p... | A | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Which of the following statements about fuzzing is/are correct? | ['Greybox fuzzing is always the better alternative to\n blackbox fuzzing.', 'Blackbox fuzzers can make use of initial seeds.', 'Greybox fuzzing keeps track of concrete program paths to\n abstract behavior.', 'Generational fuzzing requires more manual work (to specify the\n generator pol... | D | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Which of the following statements about mitigations are correct? | ['Control-Flow Integrity can efficiently protect the forward edge\n but, when using target sets, is limited on the backward edge', 'Code-Pointer Integrity (specifically the implementation\n described in the slides) uses a separate stack to protect code\n pointers.', 'Shadow stacks can b... | A | null | Document 1:::
Mitigation
Mitigation is the reduction of something harmful or the reduction of its harmful effects. It may refer to measures taken to reduce the harmful effects of hazards that remain in potentia, or to manage harmful incidents that have already occurred. It is a stage or component of emergency managemen... |
epfl-collab | Given this program snippet which is part of a large (> 10000 LoC) codebase,
which of these statements are true, given that the contents of string "s"
are attacker controlled, the attacker can run the function f only once, the
attacker has access to the binary and the binary is compiled for x86\_64 on
a ... | ['If this program is compiled with no mitigations, an attacker can\n gain remote code execution.', 'If this program is compiled with DEP (Data-Execution Prevention)\n and no other mitigation, an attacker can gain remote code execution.', 'If this program is compiled with stack canaries and no othe... | A | null | Document 1:::
C string
The C programming language has a set of functions implementing operations on strings (character strings and byte strings) in its standard library. Various operations, such as copying, concatenation, tokenization and searching are supported. For character strings, the standard library uses the con... |
epfl-collab | In x86-64 Linux, the canary is \textbf{always} different for every? | ['Namespace', 'Thread', 'Function', 'Process'] | B | null | Document 1:::
Intel 64
x86-64 (also known as x64, x86_64, AMD64, and Intel 64) is a 64-bit version of the x86 instruction set, first released in 1999. It introduced two new modes of operation, 64-bit mode and compatibility mode, along with a new 4-level paging mode. With 64-bit mode and the new paging mode, it supports... |
epfl-collab | Which of the following in Linux x86-64 assembly snippets can be used as a
gadget AND can be chained with more gadgets (e.g., in a ROP/JOP chain)? | ['\\texttt{pop rbx; pop rax; jmp rax}', '\\texttt{pop rbx; pop rax; ret}', '\\texttt{xor rbx, rbx; xor rbx, -1; push rbx; ret}', '\\texttt{mov eax, -1; call rax}'] | A | null | Document 1:::
X86 assembly language
Like all assembly languages, x86 assembly uses mnemonics to represent fundamental CPU instructions, or machine code. Assembly languages are most often used for detailed and time-critical applications such as small real-time embedded systems, operating-system kernels, and device drive... |
epfl-collab | What is the difference between C++'s \texttt{static\_cast} and \texttt{dynamic\_cast}? | ['\\texttt{static\\_cast} is faster but less safe than \\texttt{dynamic\\_cast}.', '\\texttt{static\\_cast} does not work on already-casted objects, while \\texttt{dynamic\\_cast} works always.', '\\texttt{static\\_cast} can only be applied to static classes whereas \\texttt{dynamic\\_cast} works for any class.', '\\te... | D | null | Document 1:::
Operator precedence in C
C++ also contains the type conversion operators const_cast, static_cast, dynamic_cast, and reinterpret_cast. The formatting of these operators means that their precedence level is unimportant. Most of the operators available in C and C++ are also available in other C-family langua... |
epfl-collab | Once software has been shipped, what does the Software Development Lifecycle require you to do to maintain security guarantees? | ['Provide new features to attract new users', 'Deploy updates timely and safely', 'Ensure the software works on newer machines', 'Track the evolution of third party dependencies'] | D | null | Document 1:::
Software quality
Software Assurance (SA) covers both the property and the process to achieve it: confidence that software is free from vulnerabilities, either intentionally designed into the software or accidentally inserted at any time during its life cycle and that the software functions in the intende... |
epfl-collab | You share an apartment with friends.
Kitchen, living room, balcony, and bath room are shared resources among all parties.
Which policy/policies violate(s) the principle of least privilege? | ['Different bedrooms do not have a different key.', "Nobody has access to the neighbor's basement.", 'To access the kitchen you have to go through the living room.', 'There is no lock on the fridge.'] | A | null | Document 1:::
Fair division among groups
In each department there are several faculty members, with differing opinions about which rooms are better. Two neighboring countries want to divide a disputed region among them.
Document 2:::
House allocation problem
Pareto efficiency (PE) - no other allocation is better for so... |
epfl-collab | Which of the following statement(s) is/are correct? | ['An attacker-controlled format string can lead to arbitrary write.', 'An information leak can be a preparation step of control-flow hijacking.', 'When constructing a ROP payload, we use gadgets from all currently running processes', 'In format strings, \\%n prints a hex value'] | B | null | Document 1:::
Statement (logic)
In logic and semantics, the term statement is variously understood to mean either: a meaningful declarative sentence that is true or false, or a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence.In the latter case, a statement... |
epfl-collab | Consider the following shellcode, which of the following statement(s) is/are correct?
\begin{lstlisting}[language=nasm,style=nasm]
needle: jmp gofar
goback: pop %rdi
xor %rax, %rax
movb $0x3b, %al
xor %rsi, %rsi
xor %rdx, %rdx
syscall
gofar: call goback
.string "/bin/sh"
\end{lstlisting} | ['Lines 2-6 are preparing arguments for the syscall invocation.', 'In the exploit payload, the string "/bin/sh" must end with a "0x0" byte to ensure it is terminated correctly.', 'Line 3 is not necessary.', 'The purpose of line 8 is to push the address of "/bin/sh" to the stack and jump to line 2.'] | A | null | Document 1:::
Brace expansion
Like most Unix shells, it supports filename globbing (wildcard matching), piping, here documents, command substitution, variables, and control structures for condition-testing and iteration. The keywords, syntax, dynamically scoped variables and other basic features of the language are all... |
epfl-collab | Which of the following statement(s) is/are true about Safe Exception Handling (SEH)? | ['The implementation of SEH is compiler specific.', 'SEH is a defense that protects C/C++ programs against control-flow hijack attacks through changing exception data structures.', 'Neither SafeSEH nor SeHOP checks the order and number of exception handlers.', 'SafeSEH provides stronger protection than SeHOP.'] | C | null | Document 1:::
Exception handling syntax
Exception handling syntax is the set of keywords and/or structures provided by a computer programming language to allow exception handling, which separates the handling of errors that arise during a program's operation from its ordinary processes. Syntax for exception handling va... |
epfl-collab | Which of the following statement(s) is/are true about CFI? | ['When producing valid target sets, missing a legitimate target is unacceptable.', 'Keeping the overhead of producing valid target sets as low as possible is crucial for a CFI mechanism.', 'CFI’s checks of the valid target set are insufficient to protect every forward edge control-flow transfer', 'CFI prevents attacker... | A | null | Document 1:::
Common Flash Memory Interface
The Common Flash Memory Interface (CFI) is an open standard jointly developed by AMD, Intel, Sharp and Fujitsu. It is implementable by all flash memory vendors, and has been approved by the non-volatile-memory subcommittee of JEDEC. The goal of the specification is the interc... |
epfl-collab | Assume we enforce CFI for function returns. Which of the following statements are true? | ['CFI on returns will make control-flow hijacking harder', 'CFI on returns ensures that only the single valid target is allowed', 'CFI on returns is too coarse-grained and may give the adversary sufficient valid targets for an exploit', 'CFI on returns cannot support exceptions'] | A | null | Document 1:::
Control flow analysis
In computer science, control-flow analysis (CFA) is a static-code-analysis technique for determining the control flow of a program. The control flow is expressed as a control-flow graph (CFG). For both functional programming languages and object-oriented programming languages, the te... |
epfl-collab | Which of the following statements about mitigations are true? | ['No mitigation requires hardware support to be implemented', 'The performance of certain mitigations depends on underlying architecture features (e.g., i386 versus x86-64)', 'The bug remains in the application, mitigations simply make exploitation harder', 'All mitigations fully stop an attack vector'] | C | null | Document 1:::
Mitigation
Mitigation is the reduction of something harmful or the reduction of its harmful effects. It may refer to measures taken to reduce the harmful effects of hazards that remain in potentia, or to manage harmful incidents that have already occurred. It is a stage or component of emergency managemen... |
epfl-collab | When a test fails, it means that: | ['either the program under test or the test itself has a bug, or both.', 'the test is incorrect.', 'the program under test has a bug.', 'that both the program and the test have a bug.'] | A | null | Document 1:::
High-stakes test
A high-stakes test is a test with important consequences for the test taker. Passing has important benefits, such as a high school diploma, a scholarship, or a license to practice a profession. Failing has important disadvantages, such as being forced to take remedial classes until the te... |
epfl-collab | Tick all correct answers: | ["Fuzz testing scales at least to 1'000s of lines of code.", "Formal verification scales at least upto 100'000s of lines of code.", 'Formal verification and concolic execution scale to the same extent.', 'Compiler warnings scale to millions lines of code.'] | A | null | Document 1:::
Multiple choice questions
Multiple choice (MC), objective response or MCQ (for multiple choice question) is a form of an objective assessment in which respondents are asked to select only correct answers from the choices offered as a list. The multiple choice format is most frequently used in educational ... |
epfl-collab | Which of the following statement(s) is/are true about different types of
coverage for coverage-guided fuzzing? | ['Full data flow coverage is easier to obtain than full edge coverage', 'If you cover all edges, you also cover all blocks', 'Full line/statement coverage means that every possible\n control flow through the target has been covered', 'Full edge coverage is equivalent to full path coverage\n ... | B | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Which of the following is/are true about fuzzing? | ['In structure-aware fuzzing, the mutator should only generate\n inputs that comply with all the format rules.', 'Black box fuzzing may struggle to find inputs that reach deep into the program.', 'The quality of initial seeds matters in mutational fuzzing.', 'Fuzzing is complete as soon as all code is ... | B | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Which of the following is/are true about fuzzing? | ['The efficacy of a fuzzing campaign scales with its speed (executions per second)', "Fuzzers may get ``stuck'' and cannot easily detect that they are\n no longer improving coverage", 'There is little to no benefit in running fuzzers in parallel.', 'Fuzzers generally determine the exploitability of a cras... | B | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Which of the following is/are true about fuzzing? | ['Fuzzing open-source software allows the analyst to modify the\n target software to remove parts where the fuzzer might get stuck\n (such as checksums).', 'Fuzzing can only be applied to C/C++ programs.', 'When fuzzing open-source software, recompiling it with\n mitigations... | D | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Which of the following is/are true about testing? | ['Adequate code coverage is crucial for dynamic testing.', 'False positives matter in static analyses.', 'Tests are sufficient to prove that a program is bug-free.', 'Symbolic execution is a technique of whitebox dynamic testing.'] | A | null | Document 1:::
Test method
", as well as effective and reproducible.A test can be considered an observation or experiment that determines one or more characteristics of a given sample, product, process, or service. The purpose of testing involves a prior determination of expected observation and a comparison of that exp... |
epfl-collab | Which of the following is/are true about fuzzing with sanitizers? | ['The set of sanitizers used during a fuzzing campaign must be\n carefully chosen (tradeoff between bug visibility/execution\n speed).', 'ASAN instrumentation has a negligible startup overhead.', 'Some fuzzers dynamically tweak sanitizers to speed up fuzzing.', 'Some fuzzers use fork servers... | D | null | Document 1:::
Fault injection
Robustness testing (also known as syntax testing, fuzzing or fuzz testing) is a type of fault injection commonly used to test for vulnerabilities in communication interfaces such as protocols, command line parameters, or APIs. The propagation of a fault through to an observable failure fol... |
epfl-collab | Consider the Diffie-Hellman secret-key-exchange algorithm performed in the cyclic group $(\mathbb{Z}/11\mathbb{Z}^\star, \cdot)$. Let $g=2$ be the chosen group generator. Suppose that Alice's secret number is $a=5$ and Bob's is $b=3$. Which common key $k$ does the algorithm lead to? Check the correct answer. | ['$8$', '$10$', '$7$', '$9$'] | B | null | Document 1:::
Computational Diffie–Hellman assumption
Consider a cyclic group G of order q. The CDH assumption states that, given ( g , g a , g b ) {\displaystyle (g,g^{a},g^{b})\,} for a randomly chosen generator g and random a , b ∈ { 0 , … , q − 1 } , {\displaystyle a,b\in \{0,\ldots ,q-1\},\,} it is computationally... |
epfl-collab | How many integers $n$ between $1$ and $2021$ satisfy $10^n \equiv 1 \mod 11$? Check the correct answer. | ['505', '990', '1010', '183'] | C | null | Document 1:::
Reduced residue system
In mathematics, a subset R of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r in R, R contains φ(n) elements, no two elements of R are congruent modulo n.Here φ denotes Euler's totient function. A reduced residue system modulo n can be formed fr... |
epfl-collab | You are given an i.i.d source with symbols taking value in the alphabet $\mathcal{A}=\{a,b,c,d\}$ and probabilities $\{1/8,1/8,1/4,1/2\}$. Consider making blocks of length $n$ and constructing a Huffman code that assigns a binary codeword to each block of $n$ symbols. Choose the correct statement regarding the average ... | ['It is the same for all $n$.', 'In going from $n$ to $n+1$, for some $n$ it stays constant and for some it strictly decreases.', 'None of the others.', 'It strictly decreases as $n$ increases.'] | A | null | Document 1:::
Length-limited Huffman code
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a S... |
epfl-collab | A bag contains the letters of LETSPLAY. Someone picks at random 4 letters from the bag without revealing the outcome to you. Subsequently you pick one letter at random among the remaining 4 letters. What is the entropy (in bits) of the random variable that models your choice? Check the correct answer. | ['$\\log_2(8)$', '$\\log_2(7)$', '$2$', '$\x0crac{11}{4}$'] | D | null | Document 1:::
Shannon Entropy
Named after Boltzmann's Η-theorem, Shannon defined the entropy Η (Greek capital letter eta) of a discrete random variable X {\textstyle X} , which takes values in the alphabet X {\displaystyle {\mathcal {X}}} and is distributed according to p: X → {\displaystyle p:{\mathcal {X}}\to } such... |
epfl-collab | Consider the group $(\mathbb{Z} / 23 \mathbb{Z}^*, \cdot)$. Find how many elements of the group are generators of the group. (Hint: $5$ is a generator of the group.) | ['$10$', '$2$', '$22$', '$11$'] | A | null | Document 1:::
Growth rate (group theory)
Suppose G is a finitely generated group; and T is a finite symmetric set of generators (symmetric means that if x ∈ T {\displaystyle x\in T} then x − 1 ∈ T {\displaystyle x^{-1}\in T} ). Any element x ∈ G {\displaystyle x\in G} can be expressed as a word in the T-alphabet x = a ... |
epfl-collab | In RSA, we set $p = 7, q = 11, e = 13$. The public key is $(m, e) = (77, 13)$. The ciphertext we receive is $c = 14$. What is the message that was sent? (Hint: You may solve faster using Chinese remainder theorem.). | ['$t=42$', '$t=7$', '$t=63$', '$t=14$'] | A | null | Document 1:::
RSA Cryptosystem
An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers.The security of RSA re... |
epfl-collab | Consider an RSA encryption where the public key is published as $(m, e) = (35, 11)$. Which one of the following numbers is a valid decoding exponent? | ['$5$', '$11$', '$7$', '$17$'] | B | null | Document 1:::
RSA Cryptosystem
An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers.The security of RSA re... |
epfl-collab | Let $\mathcal{C}$ be a binary $(n,k)$ linear code with minimum distance $d_{\min} = 4$. Let $\mathcal{C}'$ be the code obtained by adding a parity-check bit $x_{n+1}=x_1 \oplus x_2 \oplus \cdots \oplus x_n$ at the end of each codeword of $\mathcal{C}$. Let $d_{\min}'$ be the minimum distance of $\mathcal{C}'$. Which of... | ["$d_{\\min}' = 5$", "$d_{\\min}'$ can take different values depending on the code $\\mathcal{C}$.", "$d_{\\min}' = 6$", "$d_{\\min}' = 4$"] | D | null | Document 1:::
Linear code
The size of a code is the number of codewords and equals qk. The weight of a codeword is the number of its elements that are nonzero and the distance between two codewords is the Hamming distance between them, that is, the number of elements in which they differ. The distance d of the linear c... |
epfl-collab | Let $\mathcal{C}$ be a $(n,k)$ Reed-Solomon code on $\mathbb{F}_q$. Let $\mathcal{C}'$ be the $(2n,k)$ code such that each codeword of $\mathcal{C}'$ is a codeword of $\mathcal{C}$ repeated twice, i.e., if $(x_1,\dots,x_n) \in\mathcal{C}$, then $(x_1,\dots,x_n,x_1,\dots,x_n)\in\mathcal{C'}$. What is the minimum distanc... | ['$2n-k+1$', '$2n-2k+2$', '$2n-k+2$', '$2n-2k+1$'] | B | null | Document 1:::
Permutation codes
. , n }: σ ( i ) ≠ τ ( i ) } | {\displaystyle d(\tau ,\sigma )=|\left\{i\in \{1,2,...,n\}:\sigma (i)\neq \tau (i)\right\}|} The minimum distance of a permutation code C {\displaystyle C} is defined to be the minimum positive integer d m i n {\displaystyle d_{min}} such that there exist σ... |
epfl-collab | Consider the following mysterious binary encoding:egin{center} egin{tabular}{c|c} symbol & encoding \ \hline $a$ & $??0$\ $b$ & $??0$\ $c$ & $??0$\ $d$ & $??0$ \end{tabular} \end{center} where with '$?$' we mean that we do not know which bit is assigned as the first two symbols of the e... | ['The encoding is uniquely-decodable but not prefix-free.', 'We do not possess enough information to say something about the code.', "It does not satisfy Kraft's Inequality.", 'The encoding is uniquely-decodable.'] | D | null | Document 1:::
Binary coding
A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, ... |
epfl-collab | Suppose that you possess a $D$-ary encoding $\Gamma$ for the source $S$ that does not satisfy Kraft's Inequality. Specifically, in this problem, we assume that our encoding satisfies $\sum_{i=1}^n D^{-l_i} = k+1 $ with $k>0$. What can you infer on the average code-word length $L(S,\Gamma)$? | ["The code would not be uniquely-decodable and thus we can't infer anything on its expected length.", '$L(S,\\Gamma) \\geq H_D(S)-\\log_D(e^k)$.', '$L(S,\\Gamma) \\geq k H_D(S)$.', '$L(S,\\Gamma) \\geq \x0crac{H_D(S)}{k}$.'] | B | null | Document 1:::
Kraft–McMillan theorem
In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McMillan's version) for a given set of codeword lengths. Its applications to prefix co... |
epfl-collab | A colleague challenges you to create a $(n-1,k,d_{min})$ code $\mathcal C'$ from a $(n,k,d_{min})$ code $\mathcal C$ as follows: given a generator matrix $G$ that generates $\mathcal C$, drop one column from $G$. Then, generate the new code with this truncated $k imes (n-1)$ generator matrix. The catch is that your co... | ['$\\vec s_2$ (the all-ones vector)', '$\\vec s_1$ (the all-zeros vector).', '$\\vec s_3$ (one of the canonical basis vectors).', 'It is impossible to guarantee that dropping a column from $\\mathcal S$ will not decrease the minimum distance.'] | B | null | Document 1:::
Generator matrix
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix.
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Minimum polynomial extrapolation
. , x ... |
epfl-collab | A binary prefix-free code $\Gamma$ is made of four codewords. The first three codewords have codeword lengths $\ell_1 = 2$, $\ell_2 = 3$ and $\ell_3 = 3$. What is the minimum possible length for the fourth codeword? | ['$3$.', '$4$.', '$2$.', '$1$.'] | D | null | Document 1:::
Length-limited Huffman code
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a S... |
epfl-collab | Determine which of the following compound propositions are satisfiable (more than one answer can be correct): | ['(p → q)∧(p → ¬q)∧(¬p → q)', '(p∨¬q)∧(¬p∨q)∧(¬p∨¬q)', 'None of the other options', '(p↔q)∧(¬p↔q)'] | B | null | Document 1:::
Satisfiability problem
Satisfiability and validity are defined for a single formula, but can be generalized to an arbitrary theory or set of formulas: a theory is satisfiable if at least one interpretation makes every formula in the theory true, and valid if every formula is true in every interpretation. ... |
epfl-collab | Let P be the statement ∀x(x>-3 -> x>3). Determine for which domain P evaluates to true: | ['x>3', '-3<x<3', 'None of the other options', 'x>-3'] | A | null | Document 1:::
Planar SAT
In computer science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence graph. In other words, it asks whether the variables of a given Boolean formula—whose incidence graph consisting o... |
epfl-collab | Let p(x,y) be the statement “x visits y”, where the domain of x consists of all the humans in the world and the domain of y consists of all the places in the world. Use quantifiers to express the following statement: There is a place in the world that has never been visited by humans. | ['∀y ∀x ¬p(x,y)', '∀y ∃x ¬p(x,y)', '¬(∀y ∃x ¬p(x,y))', '∃y ∀x ¬p(x,y)'] | D | null | Document 1:::
Logical quantifier
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier ∀ {\displaystyle \forall } in the first order formula ∀ x P ( x ) {\displaystyle \forall xP(x)} expresses that everything ... |
epfl-collab | Which of the following arguments is correct? | ['Everyone who eats vegetables every day is healthy. Linda is not healthy. Therefore, Linda does not eat vegetables every day.', 'Every physics major takes calculus. Mathilde is taking calculus. Therefore, Mathilde is a physics major.', 'All cats like milk. My pet is not a cat. Therefore, my pet does not like milk.', '... | A | null | Document 1:::
Formal logic
Arguments can be either correct or incorrect. An argument is correct if its premises support its conclusion. Deductive arguments have the strongest form of support: if their premises are true then their conclusion must also be true.
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Logical argument
An argument is a series of se... |
epfl-collab | You are given the following collection of premises:
If I go to the museum, it either rains or snows.
I went to the museum on Saturday or I went to the museum on Sunday.
It did not rain and it did not snow on Saturday.
It did not rain on Sunday.
Which conclusions can be drawn from these premises ? (more than one answer ... | ['I went to the museum on Saturday.', 'I went to the museum on Sunday.', 'It snowed on Sunday.', 'It was warm on Saturday.'] | B | null | Document 1:::
A Treatise on Probability
They can't be compared. Is our expectation of rain, when we start out for a walk, always more likely than not, or less likely than not, or as likely as not?
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Formal logic
Logic studies arguments, which consist of a set of premises together with a conclusion. An examp... |
epfl-collab | Suppose we have the following function \(f: [0, 2] o [-\pi, \pi] \).
\[f(x) =
egin{cases}
x^2 & ext{ for } 0\leq x < 1\
2-(x-2)^2 & ext{ for } 1 \leq x \leq 2
\end{cases}
\] | ['\\(f\\) is bijective.', '\\(f\\) is surjective but not injective.', '\\(f\\) is not injective and not surjective.', '\\(f\\) is injective but not surjective.'] | D | null | Document 1:::
Function representation
, x n ) ≥ 0 {\displaystyle f(x_{1},x_{2},...,x_{n})\geq 0} belong to the object, and the points with f ( x 1 , x 2 , . . .
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E-function
A function f(x) is called of type E, or an E-function, if the power series f ( x ) = ∑ n = 0 ∞ c n x n n ! {\displaystyle f(x)=\sum _{... |
epfl-collab | Which of the following functions \( f :\mathbb{Z} imes \mathbb{Z} o \mathbb{Z} \) are surjective? | ['\\( f(m,n)=m \\)', '\\( f(m,n)=m+n \\)', '\\( f(m,n)=|n| \\)', '\\( f(m,n)=m^2+n^2 \\)'] | B | null | Document 1:::
Identity map
Formally, if M is a set, the identity function f on M is defined to be a function with M as its domain and codomain, satisfying In other words, the function value f(X) in the codomain M is always the same as the input element X in the domain M. The identity function on M is clearly an injecti... |
epfl-collab | Let \(A = \{a, b, c, d, ..., z\}\) be the set of lower cased English letters.
Let \(S = \{a, b, ab, cd, ae, xy, ord, ...\}\) be the set of all strings using \(A\) as an alphabet.
Given \(s\in S\), \(N(s)\) is the number of vowels in \(s\).
For example,\(N(algrzqi) = 2\), \(N(bebebe) = 3\).
We say \((s, t)\) belongs... | ['\\(R\\) is transitive.', '\\(R\\) is not an equivalence relation.', '\\(R\\) is symmetric.', '\\(R\\) is reflexive. '] | D | null | Document 1:::
Enumeration reducibility
Let lower case letters n , x . . .
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Weight (strings)
The a {\displaystyle a} -weight of a string, for a letter a {\displaystyle a} , is the number of times that letter occurs in the string. More precisely, let A {\displaystyle A} be a finite set (called the alphabet),... |
epfl-collab | If A is an uncountable set and B is an uncountable set, A − B cannot be : | ['none of the other options', 'uncountable', 'countably infinite', 'the null set'] | A | null | Document 1:::
Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natu... |
epfl-collab | You need to quickly find if a person's name is in a list: that contains both integers and strings such as:
list := ["Adam Smith", "Kurt Gödel", 499, 999.95, "Bertrand Arthur William Russell", 19.99, ...]
What strategy can you use? | ['Bubble sort the list, then use binary search.', 'Use binary search.', 'Insertion sort the list, then use binary search.', 'Use linear search.'] | D | null | Document 1:::
Rabin–Karp string search algorithm
In computer science, the Rabin–Karp algorithm or Karp–Rabin algorithm is a string-searching algorithm created by Richard M. Karp and Michael O. Rabin (1987) that uses hashing to find an exact match of a pattern string in a text. It uses a rolling hash to quickly filter o... |
epfl-collab | Let S(x) be the statement “x has been in a lake” and L(x) be the statement “x lives in Lausanne” and the domain of x consists of all the humans in the world.
The sentence : “there exists exactly one human that lives in Lausanne and that has never been in a lake” corresponds to the statement (multiple choices possible)... | ['\\( \\exists x \\Bigr[( S(x) \\wedge \neg L(x)) \\wedge \x0corall y \\left[ \neg( S(y) \\wedge \neg L(y)) \\wedge (x=y) \right] \\Bigr] \\)', '\\( \\exists x \\Bigr[ (\neg S(x) \\wedge L(x)) \\wedge \x0corall y \\left[ \neg(\neg S(y) \\wedge L(y)) \x0bee (x=y) \right] \\Bigr] \\)', '\\( \\exists! x (S(x) \\wedge L(x... | D | null | Document 1:::
Statement (logic)
In logic and semantics, the term statement is variously understood to mean either: a meaningful declarative sentence that is true or false, or a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence.In the latter case, a statement... |
epfl-collab | Let \( f : A
ightarrow B \) be a function from A to B such that \(f (a) = |a| \).
f is a bijection if: | ['\\( A= [-1, 1] \\) and \\(B= [-1, 1] \\)', '\\( A= [-1, 0] \\) and \\(B= [0, 1] \\)', '\\( A= [0, 1] \\) and \\(B= [-1, 0] \\)', '\\( A= [-1, 0] \\) and \\(B= [-1, 0] \\)'] | B | null | Document 1:::
Bijective relation
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is pai... |
epfl-collab | Let \( P(n) \) be a proposition for a positive integer \( n \) (positive integers do not include 0).
You have managed to prove that \( orall k > 2, \left[ P(k-2) \wedge P(k-1) \wedge P(k)
ight]
ightarrow P(k+1) \).
You would like to prove that \( P(n) \) is true for all positive integers. What is left for you to do... | ['None of the other statement are correct.', 'Show that \\( P(1) \\) and \\( P(2) \\) are true, then use induction to conclude that \\( P(n) \\) is true for all positive integers.', 'Show that \\( P(1) \\), \\( P(2) \\) and \\( P(3) \\) are true, then use strong induction to conclude that \\( P(n) \\) is true for all p... | C | null | Document 1:::
Idoneal number
A positive integer n is idoneal if and only if it cannot be written as ab + bc + ac for distinct positive integers a, b, and c.It is sufficient to consider the set { n + k2 | 3 . k2 ≤ n ∧ gcd (n, k) = 1 }; if all these numbers are of the form p, p2, 2 · p or 2s for some integer s, where p i... |
epfl-collab | Which of the following is equivalent to \((10001)_2\) ? (Multiple answers can be correct) | ['\\( (17)_{10} \\)', '\\( (101)_{4} \\)', '\\( (F0)_{16} \\)', '\\( (23)_{8} \\)'] | A | null | Document 1:::
Guard digit
Performing this operation gives us 2 1 × 0.0001 2 {\displaystyle 2^{1}\times 0.0001_{2}} or 2 − 2 × 0.100 2 {\displaystyle 2^{-2}\times 0.100_{2}} . Without using a guard digit we have 2 1 × 0.100 2 − 2 1 × 0.011 2 {\displaystyle 2^{1}\times 0.100_{2}-2^{1}\times 0.011_{2}} , yielding 2 1 × 0.... |
epfl-collab | Which sets are countable (Multiple answers can be correct) : | ['\\(U-C\\) with \\(U\\) an uncountable set and \\(C\\) a countable set', 'The set of string of finite length of first names starting with the letter P', 'The set of natural numbers containing at least one 3 in their decimal representation', "The set of real numbers containing at least 100 3's in their decimal represen... | B | null | Document 1:::
Countably infinite
A set S {\displaystyle S} is countable if: Its cardinality | S | {\displaystyle |S|} is less than or equal to ℵ 0 {\displaystyle \aleph _{0}} (aleph-null), the cardinality of the set of natural numbers N {\displaystyle \mathbb {N} } . There exists an injective function from S {\displays... |
epfl-collab | What is the value of \(f(4)\) where \(f\) is defined as \(f(0) = f(1) = 1\) and \(f(n) = 2f(n - 1) + 3f(n - 2)\) for integers \(n \geq 2\)? | ['45', '41', '39', '43'] | B | null | Document 1:::
Talk:Fibonacci sequence
Likewise with k = 3, we can compute every third value Fn+6 = 4Fn+3 + Fn. With k = 4, we can compute every fourth value with Fn+8 = 7Fn+4 − Fn. —Quantling (talk | contribs) 15:01, 10 May 2023 (UTC) Apply the roots of unity filter to the GF to get the GF for the multisection.
Documen... |
epfl-collab | Which of the following are true regarding the lengths of integers in some base \(b\) (i.e., the number of digits base \(b\)) in different bases, given \(N = (FFFF)_{16}\)? | ['\\((N)_4\\) is of length 12', '\\((N)_4\\) is of length 4', '\\((N)_2\\) is of length 16', '\\((N)_{10}\\) is of length 40'] | C | null | Document 1:::
Digit sum
Let n {\displaystyle n} be a natural number. We define the digit sum for base b > 1 {\displaystyle b>1} , F b: N → N {\displaystyle F_{b}:\mathbb {N} \rightarrow \mathbb {N} } to be the following: F b ( n ) = ∑ i = 0 k d i {\displaystyle F_{b}(n)=\sum _{i=0}^{k}d_{i}} where k = ⌊ log b n ⌋ {\d... |
epfl-collab | In a lottery, a bucket of 10 numbered red balls and a bucket of 5 numbered green balls are used. Three red balls and two green balls are drawn (without replacement).
What is the probability to win the lottery? (The order in which balls are drawn does not matter). | ['$$\x0crac{1}{1900}$$', '$$\x0crac{1}{1200}$$', '$$\x0crac{1}{7200}$$', '$$\x0crac{1}{14400}$$'] | B | null | Document 1:::
Lottery mathematics
Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based primarily on combinatorics, particularly the twelvefold way and combinations without replacement.
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Randomness
For example, with a bowl containing just 10 red marbles and... |
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