If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)= 3 2 P(A) and P(C)= 1 2 P(B) , then P(A C) equals

Step-by-step solution

Since A, B, and C are mutually exclusive and exhaustive events, the sum of their probabilities is P(A) + P(B) + P(C) = 1 . Given P(B) = 3 2 P(A) and P(C) = 1 2 P(B) , we can express P(C) in terms of P(A) as P(C) = 1 2 ( 3 2 P(A) ) = 3 4 P(A) . Substituting these into the sum equation: P(A) + 3 2 P(A) + 3 4 P(A) = 1 . Finding a common denominator: 4 P(A) + 6 P(A) + 3 P(A) 4 = 1 , which simplifies to 13 4 P(A) = 1 . Thus, P(A) = 4 13 . Then P(B) = 3 2 4 13 = 6 13 and P(C) = 3 4 4 13 = 3 13 . Since A and C are mutuall