If are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is

Question

Philoid · Accepted Answer

As 3 events are mutually exclusive and exhaustive.

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

⇒

⇒ 5 + 3p = 6

∴ p = 1/3

As 1/3 lies in both intervals given in option (a) and (d)

But a larger value like 100 which comes if we choose option d can make P(A) < 0 which is not possible.

∴ Option (a) is the most suitable choice here.