Three soldies, X, Y and Z have probabilities \(\frac{1}{3}, \frac{1}{5}\) and \(\frac{1}{4}\) respectively of hitting a target. If each of them fires once, ...
Question 1 Report
Three soldies, X, Y and Z have probabilities \(\frac{1}{3}, \frac{1}{5}\) and \(\frac{1}{4}\) respectively of hitting a target. If each of them fires once, find, correct to two decimal places, the probability that only one of them hits the target
Answer Details
Hit probabilities: \(P(X)=\tfrac13,\ P(Y)=\tfrac15,\ P(Z)=\tfrac14\); miss probabilities: \(\tfrac23,\tfrac45,\tfrac34\). "Only one hits" means exactly one succeeds while the other two miss (events independent):
\[P(\text{only }X)=\frac13\cdot\frac45\cdot\frac34=\frac{12}{60}=\frac15,\] \[P(\text{only }Y)=\frac23\cdot\frac15\cdot\frac34=\frac{6}{60}=\frac{1}{10},\] \[P(\text{only }Z)=\frac23\cdot\frac45\cdot\frac14=\frac{8}{60}=\frac{2}{15}.\]Adding (LCD 30):
\[P(\text{exactly one})=\frac{6}{30}+\frac{3}{30}+\frac{4}{30}=\frac{13}{30}\approx 0.43.\]Download The App On Google Playstore
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