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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`
Solution
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`.
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