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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
- mutually exclusive
- independent.
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Solution
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`
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