Let A, B , and C be three independent events with P(A)=13,P(B)=12, and

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Let A, B , and C be three independent events with

P (A) = \frac{1}{3}, P (B) = \frac{1}{2}, a n d P (C) = \frac{1}{4} .

. The probability of exactly 2 of these events occurring, is equal to

Options:

A . 14

B . 724

C . 34

D . 1724

Answer: Option A
:
A
P(exactly two of A, B and C) = P(AB) + P(BC) + P(CA) – 3 P(ABC)
Since A, B ,C are independent events,
Required probability = P(A)P(B) + P(B)P(C) +P(C)P(A) – 3 P(A)P(B)P(C)

= \frac{1}{3} \times \frac{1}{2} + \frac{1}{2} \times \frac{1}{4} + \frac{1}{4} \times \frac{1}{3} - 3 \frac{1}{3} \times \frac{1}{2} \times \frac{1}{4} = \frac{1}{4.}

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