Question

Given that the events A and B are such that `P(A) = 1/2, PA∪B=3/5 and P (B) = p`. Find p if they are

1. mutually exclusive
2. independent.

Answer 1

i. Since the events are mutually exclusive.

∴ P(A ∩ B) = 0

again P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

∴ `3/5 = 1/2 + p - 0`

⇒ p = `3/5 - 1/2 = (6 - 5)/10 = 1/10`

ii. The events are independent.

∴ P(A ∩ B) = P(A) . P(B)

= `1/2 . p`

again P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

and  `3/5 = 1/2 + p - 1/2 p`

or `1/2 p = 3/5 - 1/2 = (6 - 5)/10 = 1/10`

⇒ p = `2/10 = 1/5`