Let A, B , and C be three independent events with P(A)=13,P(B)=12,andP(C)=14. . The probability of exactly 2 of these events occurring, is equal to
A
14
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B
724
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C
34
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D
1724
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Solution
The correct option is A14 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) =13×12+12×14+14×13−313×12×14=14.