JEE Mains · Maths · STD 11 - 14. probability
Three persons \(P, Q\) and \(R\) independently try to hit a target . If the probabilities of their hitting the target are \(\frac{3}{4},\frac{1}{2}\) and \(\frac{5}{8}\) respectively, then the probability that the target is hit by \(P\) or \(Q\) but not by \(R\) is
- A \(\frac{{21}}{{64}}\)
- B \(\frac{{9}}{{64}}\)
- C \(\frac{{15}}{{64}}\)
- D \(\frac{{39}}{{64}}\)
Answer & Solution
Correct Answer
(A) \(\frac{{21}}{{64}}\)
Step-by-step Solution
Detailed explanation
Required probability \(=\left(\frac{3}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)+\left(\frac{1}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)+\left(\frac{3}{4}\right)\left(\frac{1}{2}\right)\left(\frac{3}{8}\right)\) \(=\frac{12+9}{64}=\frac{21}{64}\)
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