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856
help-10
ed49a73217d84786ad614bd512f6966b
716,143,555,193,733,100
HSUUUSS
02/23/2022 17:19:55
thanks for your help guys 🙂
1
0
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null
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856
help-10
ed49a73217d84786ad614bd512f6966b
716,143,555,193,733,100
HSUUUSS
02/23/2022 17:19:57
.close
1
0
null
null
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:09:28
https://cdn.discordapp.c…4886/unknown.png
unknown.png
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:10:01
so, the probability of the first draw is 1/5
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:10:22
the probability of the 2nd draw - you can pull out the first one again, or 20 that aren't broken
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:10:27
so that's 21/25
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:10:38
and then the 3rd draw has to be one of the 4 that hasn't been pulled
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:10:40
so 4/25
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:10:59
multiply those... and i get an answer that isn't correct (they give us answers but not methods)
1
0
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:11:04
what is wrong here?
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:26:54
@Helpers
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:27:09
i have like 5 more that i'd like help with 😦
1
0
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help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:33:33
do you think that the defective light bulbs are labeled? "second defective light bulb is ..."
0
1
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:34:19
that's what i'm assuming what they are implying
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:35:10
so why the probability of the first draw is 1/5 ?
0
1
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:35:35
5 defective lightbulbs, 25 total
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:35:43
so getting a defective one on the first draw: 1/5
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:35:54
werent the bulbs enumerated ?
0
1
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help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:36:06
"second defective light bulb"
0
1
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:36:24
honestly, i have no idea how to interpret it
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:38:57
ok sorry i'm not an english speaker i think i understand this question now and why your answer is wrong.
0
1
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help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:41:22
a )the product rule (prob a * prob b * prob c) is sensible to the order, so 1/5 (probability of pulling of a defective one )
0
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:42:07
ok yes
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:43:37
4/5 (probability of pulling off a nice one)
0
1
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help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:45:03
so i'm interpreting the question like this, in your first 3 extractions you have to retrieve 2 defective, and 1 in good shape
0
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:45:35
yeah
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:46:13
ok i have it
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:46:21
it's 1/5 * 20/25 * 1/5
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:46:23
plus
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:46:29
20/25 * 1/5 * 1/5
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:46:33
with the restrain that in your third extraction you have to retrieve the third one
0
1
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:46:34
yes
0
1
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:46:37
the third draw needs to be 1/5
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:46:50
so the only change in order is in the first ones
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:46:54
exaclty
0
1
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:47:00
is that correct?
0
1
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:47:05
ok so these questions are written by a non-native speaker and his english is NOT good.
1
0
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:47:07
yeah it is
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:47:41
fine, the part b) is similar but in these cases you are not replacing the bulbs
0
1
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:48:00
yeah
1
0
null
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null
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:49:07
so 1/5*20/24 * 4/23 + 4/5* 5/24*4/23
0
1
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:49:26
yeah that's what i got here too
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:49:39
awesome, thank you - i knew i was missing something and that product rule thing was it
1
0
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help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:49:55
nice dude i'm glad to hear that
0
1
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857
help-10
4fff2485755543d389e32937d9b97361
738,072,502,881,878,100
BillyElKid
11/07/2021 15:50:01
🙂
0
1
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:50:48
yeah see, i just checked that answer and it's correct
1
0
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:52:03
ok i'm gonna stop now, i've been at this all day and i've done more than enough i feel like
1
0
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help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:52:06
thank you for your help
1
0
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857
help-10
4fff2485755543d389e32937d9b97361
260,073,142,553,280,500
JCtheMC
11/07/2021 15:52:07
.close
1
0
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
510,789,298,321,096,700
TeXit
02/23/2022 17:42:13
**Yeetus**
https://cdn.discordapp.c…522029678612.png
842836522029678612.png
1
0
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:42:49
Doesn’t make any sense
0
1
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:42:59
Looks like E is a subset of X right?
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:43:10
But S is a subset of P(X)
0
1
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:43:32
Oh nvm
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:43:43
I didn’t see “collection of”…
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:44:18
Oh so you need to prove two things
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:44:50
Proving first, that S’=collection of subsets having that form, is a sigma algebra containing Y and {Z}
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:45:26
Next proving any sigma algebra T containing Y and {Z}, S’ is contained in T
0
1
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:45:36
Proving those two things I think
0
1
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:46:30
The second is trivial right
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:46:37
That leaves us the first one
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:46:51
Proving S’ is a sigma algebra
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:48:03
No
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:48:14
You only need to prove S’ is a sigma algebra now
0
1
null
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:50:05
Originally You want to prove that S’ is the minimal sigma algebra generated by Y union {Z}, which is equivalent to it being the minimal sigma algebra containing Y union {Z} , which is equivalent to it being the intersection of all sigma algebra containing Y union {Z}
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:50:41
That’s why you need to prove the following two things, and the second one is trivial
0
1
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:51:24
Doing with you
0
1
null
null
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:55:49
No something missed
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:56:03
Actually three things I put the first two together
0
1
null
null
null
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:56:15
1, S’ contains Y union {Z}
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:56:24
2, S’ is a sigma algebra
0
1
null
null
null
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null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:56:44
3, for any sigma algebra T containing Y union {Z}, T contains S’
0
1
null
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858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:56:49
And 3 is trivial
0
1
null
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null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:56:57
Maybe 1 is also trivial
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:58:38
Yeah 1 is also trivial
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 17:59:53
Any A from Y , A=AnZ union An Z^c
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:00:13
And Z=XnZ union empty n Z^c
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:01:42
Any non empty sigma algebra of X must contain X and empty
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:04:02
Yeah only 2 left
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:05:03
Yeah that’s the only thing left to be done
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:05:59
We do it by definition I think
0
1
null
null
null
null
null
858
help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:06:14
Just proving it satisfies what a sigma algebra should satisfy
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:06:44
Complementation , countable union or intersection
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:08:24
?
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:09:06
You need to prove that the complementation of AnZ union BnZ^c must also be of this form
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:09:22
By definition
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:13:47
Yeah
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:13:52
By definition
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:15:53
Idk, but
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:16:03
It’s the only thing left cause I found
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:16:10
Countable union is easy
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:17:46
Countable union of (A_k nZ)U(B_k n Z^c) is (AnZ)U(BnZ^c) where A / B is the countable union of A_k / B_k respectively
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:17:52
So only complementation left
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:25:21
Using algebra now
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:28:02
AZ+B(1+Z)+AZB(1+Z)+1=AZ+B+BZ+AZB+AZB+1=AZ+BZ+B+1 and I need to write it as some EZ+F(Z+1)+EFZ(Z+1)=EZ+FZ+F
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:29:03
No a union b is a+b+ab
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:29:15
Complement of a = 1+a
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:29:47
Nvm I still need to translate back into set theory anyway
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:35:36
I got it
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help-10
8cfb7dbdcbba4038ae8ae6a71026c774
826,318,983,413,366,800
Cogwheels of the mind
02/23/2022 18:36:06
It is (A^c n Z)U(B^c n Z^c)
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