Question

If two events A and B are such that P(A) = 1/2, P(B) = 1/3 and P(A ∪ B) = 2/3. Show that A and B are mutually independent.

Answer 1

For set A & B, addition theorem is given by

P(A ∩ B) = P(A) + P(B) - P(A ∩ B)

2/3 = (1/2) + (1/3) - P(A ∩ B)

∴ P(A ∩ B) = (1/2) + (1/3) - (1/2) = 1/6

Now, P(A ∩ B) = 1/6 = (1/2).(1/3) = P(A).P(B)

So, A & B are mutually independent.