First slide

Theorems of probability

Question

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

Moderate

A

$\frac{235}{256}$
B

$\frac{21}{256}$
C

$\frac{3}{256}$
D

$\frac{253}{256}$

Solution

Given that the probability of hitting a target independently by four persons are respectively
$P (A) = \frac{1}{2}, P (B) = \frac{3}{4}, P (C) = \frac{1}{4}, P (D) = \frac{1}{8}$
The probability of hitting the target
= 1-P(not hitting the target)
$= 1 - P (\bar{A}) P (\bar{B}) P (\bar{C}) P (\bar{D})$
$= 1 - \frac{1}{2} \frac{1}{4} \frac{3}{4} \frac{7}{8} = 1 - \frac{21}{256} = \frac{235}{236}$

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