WAEC - Further Mathematics (2006 - No. 31)

A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap B) = \frac{1}{15}\). Find \(P(B)\).

\(\frac{3}{5}\)

\(\frac{1}{3}\)

\(\frac{1}{6}\)

\(\frac{2}{15}\)

For independent events A and B, \(P(A \cap B) = P(A) \times P(B)\)

\(\frac{1}{15} = \frac{2}{5} \times P(B)\)

\(P(B) = \frac{1}{15} \div \frac{2}{5}\)

\(P(B) = \frac{1}{6}\)