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Stuck on tough probability question

N people are interviewed, where N is even. Each person is given a card, selected from a random N cards, half of which contain an embarrassing question the other half which contain a question - 'is your birthday between January and June inclusive?'

Suppose that of the N people interviewed, R answered 'yes' to the question they received. Let Y be the event that a person says 'yes', and E the event they got a card with an embarrassing question. Assuming that half the population have birthdays between Jan and June inclusive, write down P(Y), P(E) and P(Y l E(compliment)) (last one is Y given E compliment). I would have though P(Y) is R/N and p(E) is 1/2...then using the law of total probability I get some equation involving E given Y or Y given E, and am stuck. I may have gone wrong with P(y) or P(E). I'm getting confused as to what is conditional on what! Any help would be appreciated :biggrin:
Original post by Student10011
...


Seems OK so far.

Your equation should be:

P(Y)=P(Y∣E)P(E)+P(Y∣EC)P(EC)P(Y)=P(Y|E)P(E) + P(Y|E^C)P(E^C)

And just sub in the values.

I presume you're looking for P(Y|E) - you've not said.
(edited 9 years ago)
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Student10011
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Original post by ghostwalker
Seems OK so far.

Your equation should be:

P(Y)=P(Y∣E)P(E)+P(Y∣EC)P(EC)P(Y)=P(Y|E)P(E) + P(Y|E^C)P(E^C)

And just sub in the values.

I presume you're looking for P(Y|E) - you've not said.


Yeah that's the part I'm stuck on. Can't work out what P(Y l E) actually is! Edit. actually I think I can work it out now, if I'm correct in thinking that P(y l E compliment) = 1/2
(edited 9 years ago)
Original post by Student10011
Yeah that's the part I'm stuck on. Can't work out what P(Y l E) actually is! Edit. actually I think I can work it out now, if I'm correct in thinking that P(y l E compliment) = 1/2


Yes, P(Y∣EC)=0.5P(Y|E^C)=0.5

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