SOLUTION: Given that for two events A and B,P(A)=3/5,P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?

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Question 1056339: Given that for two events A and B,P(A)=3/5,P(B)=2/3
and P(A union B) =3/4, what is P(A|B)?

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Given that for two events A and B,P(A)=3/5,P(B)=2/3
and P(A union B) =3/4, what is P(A|B)?

P(A|B) = P(A&B)/P(B)

So first we have to find P(A&B)

P(AUB) = P(A) + P(B) - P(A&B)

3/4 = 3/5 + 2/3 - P(A&B)

Multiply through by 60

45 = 36 + 40 - 60P(A&B)

45 = 76 - 60P(A&B)

-31 = -60P(A&B)

31/60 = P(A&B)

Go back to 

P(A|B) = P(A&B)/P(B)

P(A|B) = (31/60)/(2/3)

P(A|B) = (31/60)(3/2)

P(A|B) = 31/40

Edwin

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