Question

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 ______.

Options

• `1/11`

• `2/11`

• `5/11`

• `6/11`

Answer 1

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 `2/11`.

Explanation:

Let 3P(A) = 2P(B) = P(C) = P

Which gives P(A) = `P/3`

P(B) = `P/2`

And P(C) = P

Now since A, B, C are mutually exclusive and exhaustive events

We have P(A) + P(B) + P(C) = 1

⇒ `P/3 + P/2 + p` = 1

⇒ P = `6/11`

Hence, P(A) = `P/3 = 2/11`.