S1 - simple probability problem

Could anyone help me with this problem? Its from solomon paper A

The events A and B are such that
P(A)=5/16 P(B)=(1/2) and P(A|B)=(1/4)
Find
a) P(A n B) <===yes, I know the symbol is wrong
For this I just multiplied (1/4) and (1/2) and got (1/8)

b) P(B'|A)
I can't get the right answer to this question. I know it's a very simple question but the answer that I get doesn't match with the answer sheet given to us
It should be (3/5)

Thanks in advance ^-^

Reply 1

username9303

Just use the conditional probability equation.

Reply 2

m:)ckel

...and also draw a Venn diagram

From that it'll be clear to see that P(B' n A) = P(A) - P(A n B)

Reply 3

danniella

Hello!

First part:
P(A/B) = P(AnB)/P(B)
So P(AnB)=P(A/B)P(B)
P(AnB)=(1/4)x(1/2)=1/8

Second part:
P(B'/A)=P(B'nA)/P(A)

Now P(B'nA) + P(BnA) = P(A)
(Everything that's not in B but is in A, together with everything that's in both B and A, gives you the whole of A. If something's in A, then either it's in B as well (AnB) or it isn't in B (AnB') )

So P(B'nA) = P(A) - P(BnA)

and P(BnA) = P(AnB)

So P(B'nA) = (5/16) - (1/8) = 3/16

So now P(B'/A) = P(B'nA)/P(A) = 3/16 divided by 5/16 = 3/5

love Danniella

Reply 4

Jess_Sedai

Thanks everyone ^^
(+ve rep of course)

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