Let X and Y be two events such that P(X) = 1/3, P(X/Y) = 1/2 and P(Y/X) = 2/5. Then P(X∪Y) = 2/5, P(Y) = 4/15, P(X'|Y) = 1/2, P(X∩Y) = 1/5

The correct options are B P(Y) = 4/15 and C P(X'|Y) = 1/2

Given that:
P(X) = 1/3, P(X/Y) = 1/2 and P(Y/X) = 2/5

Now, we know that:
P(Y/X)P(X) = P(X∩Y)
P(X∩Y) = (2/5) × (1/3) = 2/15

P(Y) = P(X∩Y) / P(X/Y) = (2/15) / (1/2) = 4/15

Now,
P(X∪Y) = P(X) + P(Y) − P(X∩Y) = 1/3 + 4/15 − 2/15 = 1/3 + 2/15 = 7/15
P(X∪Y) = 7/15

P(X'|Y) = P(X'∩Y) / P(Y) = [P(Y) − P(X∩Y)] / P(Y) = 1 − P(X/Y) = 1 − 1/2 = 1/2

Hence, the correct options are B and C.