Bayes' Theorem

E

Ethan3141

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This is a question from a mock exam I have. I have managed to get answers for b, c and d (0.6178, 0.5036 and 0.2907) that I think make sense. Anyway I need help with part a I have no concrete idea of what it is wanting from me. The one thing I have considered is stating what P(A), P(B), P(A|B) and P(B|A) are in this context but I don't know what these could be since there isn't anything to extract them from.

In short, I am confused what the question wants/how to start it. Any guidance would be greatly appreciated.

Thanks, Ethan.
 
The respective percentages are given (50, 60, and 70) for particular stores, probabilities of being Woman given a Store (A, B, or C). For the first, per example P(W|A)=0.5. you can also give P(A), P(B) and P(C)

To get b) you will have to work out how many women in total, that is 25 from A, 45 from B and 70 from C. The probability of choosing a woman is the total of women over the total of employees.

On c) you can use the Theorem, but also note that from the total of 140 Woman, exactly 70 are in C. Either way, you will get the same.
 
raquelc said:
The respective percentages are given (50, 60, and 70) for particular stores, probabilities of being Woman given a Store (A, B, or C). For the first, per example P(W|A)=0.5. you can also give P(A), P(B) and P(C)

To get b) you will have to work out how many women in total, that is 25 from A, 45 from B and 70 from C. The probability of choosing a woman is the total of women over the total of employees.

On c) you can use the Theorem, but also note that from the total of 140 Woman, exactly 70 are in C. Either way, you will get the same.
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This sounds good in regards to (b) and (c) (aka I am more confident I approached them correctly). However, I still don't understand part A (I am assuming the first part of this answer is referring to it, but if it isn't and I misinterpreted you then just ignore this) Are you saying that I should just state all the probabilities. Again sorry if I have misinterpreted you and thank you for the help :)
 
You can state the probabilities and give the general formula of P(A|W)=P(W|A)*P(A)/P(W) stating the meaning of each.
I'd suggest double-checking your answers for b,c, and d, as they aren't accurate (maybe is due to rounding)
 
raquelc said:
You can state the probabilities and give the general formula of P(A|W)=P(W|A)*P(A)/P(W) stating the meaning of each.
I'd suggest double-checking your answers for b,c, and d, as they aren't accurate (maybe is due to rounding)
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Interesting, I did round b to 4dp and all subsequent answers. I just noticed when calculating (b) I forgot to subtract the 1 from the denominator (I only subtracted from the numerator for some reason). My new answers are: (b) 139/224 = 0.6205 (4dp), (c) 3136/6255 = 0.5014 (4dp), (d) 224/765 = 0.2928 (4dp). I hope these answers are more accurate. Thanks for pointing out my lack of accuracy and just in general the help you have given me. One last clarification please, for the P(A|W) the W is whether they are/aren't women and the A is the case of them working in store A, B or C? Thanks again :)
 
Yes, that is absolutely right.
I'd have to apologize, as I have considered the woman that resigns on the working out. On that note, maybe you could include P(W|R)=0.5. As that would be the probability of being a Woman given that resigns.
Hmm...that makes me think that what asks on a) is related with that and maybe P(W|R)=P(R|W)*P(W)/P(R) would be the context described
Sorry if I am giving more confusion to this. Interesting question
 
raquelc said:
Yes, that is absolutely right.
I'd have to apologize, as I have considered the woman that resigns on the working out. On that note, maybe you could include P(W|R)=0.5. As that would be the probability of being a Woman given that resigns.
Hmm...that makes me think that what asks on a) is related with that and maybe P(W|R)=P(R|W)*P(W)/P(R) would be the context described
Sorry if I am giving more confusion to this. Interesting question
Click to expand...
No you're not adding confusion, I think you might be right regarding to part a as it seems unreasonable for the person who wrote the question to just randomly add 'one woman employee resigns' at the end. Never the less to be safe if a question like part a comes up on the exam I am going to go overkill and include all unless it is more clear on what it wants. Thanks for the help really appreciate it :)
 
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