Question

A and B are independent events. Probability that both A and  B occur is (1/8). Probability that neither of them occur is (3/8). Probability of occurrence of A is ______

(a) (3/4)

(b) (1/3)

(c) (1/4) 

(d) (2/3)

Answer 1

The correct option (c) (1/4)

Explanation:

 given: P(A ∩ B) = (1/8) and P(A' ∩ B') = (3/8)

∵ independent event

⇒ P(A) ∙ P(B) = (1/8) and P(A') ∙ P(B') = (3/8) .......... P(A) = x and P(B) = y

∴ xy = (1/8) and (1 – x)(1 – y) = (3/8)

∴ 1 – y – x + xy = (3/8)

∴ 1 – (x + y) = (2/8)

∴ x + y = (6/8) = (3/4) 

putting y = (1/8x)

∴ x + (1/8x) = (3/4)

∴ 4(8x² + 1) = 24x

∴ 32x² – 24x + 4 = 0

∴ 8x² – 6x + 1 = 0

∴ x = (1/2) or x = (1/4) i.e. P(A) = (1/4).