If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3P(A) = 2P(B) = P(C), then P(A) is equal to

Question

Philoid · Accepted Answer

Given,

3P(A) = 2P(B) = P(C) = k(say)

∴ P(A) = k/3

P(B) = k/2

And P(C) = k

As events A,B and C are mutually exclusive and exhaustive,

∴ P(A ∪ B ∪ C) = P(A) + P(B) + P(C) = 1

⇒ 1 = k/3 + k/2 + k

⇒ 1 =

⇒ k = 6/11

As, P(A) = k/3 =

Our answer matches with option (b)

∴ Option (b) is the only correct choice