A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap...
FURTHER MATHEMATICS
WAEC 2006
A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap B) = \frac{1}{15}\). Find \(P(B)\).
- A. \(\frac{3}{5}\)
- B. \(\frac{1}{3}\)
- C. \(\frac{1}{6}\)
- D. \(\frac{2}{15}\)
Correct Answer: C. \(\frac{1}{6}\)
Explanation
For independent events A and B, \(P(A \cap B) = P(A) \times P(B)\)
\(\frac{1}{15} = \frac{2}{5} \times P(B)\)
\(P(B) = \frac{1}{15} \div \frac{2}{5}\)
\(P(B) = \frac{1}{6}\)
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