Given that the events A and B are such that P(A) = 1/2, P (A ∪ B) = 3/5 and P(B) = p. Find p if they are (i) mutually exclusive (ii) independent.

Given: P(A) =, P (A ∪ B) =and P(B) = p

(i) mutually exclusive

When A and B are mutually exclusive.

Then (A ∩ B) = ϕ

⇒ P (A ∩ B) = 0

As we know, P (A ∪ B) = P(A) + P(B) - P (A ∩ B)

⇒

⇒

(ii) independent

When A and B are independent.

⇒ P (A ∩ B) = P(A) . P(B)

⇒ P (A ∩ B) =

As we know, P (A ∪ B) = P(A) + P(B) - P (A ∩ B)

⇒

⇒

⇒

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