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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