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.

$1$

$\frac{1}{2}$

$\frac{5}{12}$

$\frac{1}{12}$

View answer & explanation

Correct answer is C

$p(P) = \frac{1}{2}, p(P') = \frac{1}{2}$

$p(Q) = \frac{1}{3}, p(Q') = \frac{2}{3}$

$p(R) = \frac{3}{4}, p(R') = \frac{1}{4}$

p(exactly two hit the target) = p(P and Q and R') + p(P and R and Q') + p(Q and R and P')

= $(\frac{1}{2} \times \frac{1}{3} \times \frac{1}{4}) + (\frac{1}{2} \times \frac{3}{4} \times \frac{2}{3}) + (\frac{1}{3} \times \frac{3}{4} \times \frac{1}{2})$

= $\frac{1}{24} + \frac{6}{24} + \frac{3}{24}$

= $\frac{5}{12}$

See all Further Mathematics questions & answers

See more WAEC questions & answers

Aptitude Tests

Data Interpretation Questions and Answers

Personality Test

Puzzles Questions and Answers

Typing Speed and Accuracy Test

Logical Reasoning Questions and Answers

Microsoft Office Questions and Answers

Nigeria General Knowledge Questions and Answers

Situational Judgement Questions and Answers

Verbal Reasoning Questions and Answers

Spatial Reasoning Questions and Answers

Numerical Reasoning Questions and Answers

Quantitative Reasoning Questions and Answers

Abstract Reasoning Questions and Answers

See all →

View latest jobs in Nigeria today

Three men, P, Q and R aim at a target, the probabilities that P, Q and R hit the target are 12\frac{1}{2}, 13\frac{1}{3} and 34\frac{3}{4} respectively. Find the probability that exactly 2 of them hit the target.

Similar Questions

Aptitude Tests

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.