X and Y are two independent event. If \(P(X) = \frac{1}{5}\) and \(P(X \cap Y)...
FURTHER MATHEMATICS
WAEC 2007
X and Y are two independent event. If \(P(X) = \frac{1}{5}\) and \(P(X \cap Y) = \frac{2}{15}\), find \(P(Y)\).
- A. \(\frac{2}{3}\)
- B. \(\frac{2}{5}\)
- C. \(\frac{1}{3}\)
- D. \(\frac{1}{5}\)
Correct Answer: A. \(\frac{2}{3}\)
Explanation
For independent events \(P(X \cap Y) = P(X) \times P(Y)\)
\(\frac{2}{15} = \frac{1}{5} \times P(Y)\)
\(P(Y) = \frac{2}{15} ÷ \frac{1}{5} = \frac{2}{3}\)
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