A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B)=4P(A) and 3P(C)=2P(B), then what is P(A) equal to?

Explanation

Let P(B) = x. Then P(A) = \frac{3}{4}x and P(C) = \frac{2}{3}x. Since the events are mutually exclusive and exhaustive, P(A) + P(B) + P(C) = 1. Substituting gives \frac{3}{4}x + x + \frac{2}{3}x = 1. Getting a common denominator of 12 yields \frac{9x + 12x + 8x}{12} = 1, so 29x = 12 \implies x = \frac{12}{29}. Thus, P(A) = \frac{3}{4}(\frac{12}{29}) = \frac{9}{29}.

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