Three men, P, Q and R aim at a target, the probabilities that P, Q...
FURTHER MATHEMATICS
WAEC 2009
Three men, P, Q and R aim at a target, the probabilities that P, Q and R hit the target are \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{3}{4}\) respectively. Find the probability that exactly 2 of them hit the target.
- A. \(1\)
- B. \(\frac{1}{2}\)
- C. \(\frac{5}{12}\)
- D. \(\frac{1}{12}\)
Correct Answer: C. \(\frac{5}{12}\)
Explanation
\(p(P) = \frac{1}{2}, p(P') = \frac{1}{2}\)
\(p(Q) = \frac{1}{3}, p(Q') = \frac{2}{3}\)
\(p(R) = \frac{3}{4}, p(R') = \frac{1}{4}\)
p(exactly two hit the target) = p(P and Q and R') + p(P and R and Q') + p(Q and R and P')
= \((\frac{1}{2} \times \frac{1}{3} \times \frac{1}{4}) + (\frac{1}{2} \times \frac{3}{4} \times \frac{2}{3}) + (\frac{1}{3} \times \frac{3}{4} \times \frac{1}{2})\)
= \(\frac{1}{24} + \frac{6}{24} + \frac{3}{24}\)
= \(\frac{5}{12}\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *