If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B)...
FURTHER MATHEMATICS
WAEC 2008
If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B) = \frac{1}{4}\), find P(B).
- A. \(\frac{3}{7}\)
- B. \(\frac{4}{7}\)
- C. \(\frac{5}{7}\)
- D. \(\frac{6}{7}\)
Correct Answer: A. \(\frac{3}{7}\)
Explanation
\(P(A) = \frac{7}{12}\)
\(P(A \cap B) = \frac{1}{4} = P(A) \times P(B)\) (Independent events)
\(\frac{1}{4} ÷ \frac{7}{12} = \frac{1}{4} \times \frac{12}{7} \)
= \(\frac{3}{7}\)
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