A, B and C are three mutually exclusive and exhaustive events. P(A) = 2P(B) = 6P(C). Find P(B).
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.3
Events that are mutually exclusive and exhaustive cannot happen together and between them cover every outcome, so their probabilities add up to 1.
Let \(P(C)=k\); then \(P(A)=6k\) and \(2P(B)=6k\), so \(P(B)=3k\)
The three probabilities add up to 1: \(6k+3k+k=1\), so \(k=0.1\)
Hence \(P(B)=3k=0.3\)