Two events A and B in a sample space are mutually exclusive and exhaustive. If P(A) = 1/3, find P(B).

Question

Two events A and B in a sample space are mutually exclusive and exhaustive. If P(A) = \(\frac{1}{3}\) find P(B).

Answer 1

A and B are mutually exclusive and exhaustive events.

∴ P(A) + P(B) = 1 (Putting P(A) = \(\frac{1}{3}\))
\(\frac{1}{3}\) + P(B) = 1

∴ P(B) = 1 – \(\frac{1}{3} = \frac{2}{3}\)