P(A) = 2/3; P(B) = 3/5; P(A∪B) = 5/6. Find P(B/A)(a) 11/20(b) 13/20(c) 13/18(d) 15/20

To find P(B/A), we need to use the formula for conditional probability which is P(B/A) = P(A ∩ B) / P(A).

We know P(A), P(B), and P(A ∪ B), but we don't know P(A ∩ B). However, we can find P(A ∩ B) using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Let's find P(A ∩ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) 5/6 = 2/3 + 3/5 - P(A ∩ B) 5/6 = 10/15 + 9/15 - P(A ∩ B) 5/6 = 19/15 - P(A ∩ B) P(A ∩ B) = 19/15 - 5/6 P(A ∩ B) = 19/15 - 15/18 P(A ∩ B) = 114/270 - 75/270 P(A ∩ B) = 39/270 = 13/90

Now we can find P(B/A):

P(B/A) = P(A ∩ B) / P(A) P(B/A) = (13/90) / (2/3) P(B/A) = (13/90) * (3/2) P(B/A) = 39/180 = 13/60

So, the answer is not in the options given. There might be a mistake in the problem or in the options provided.