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

A
1/192
B
25/32
C
25/192
D
7/32

Solution:

Let $A, B, C$ and $D$ be the persons that hit the target independently.

$∴ P$ (The target would be hit)

$\begin{array}{l} = 1 - P (none of them hits) = 1 - P (\bar{A} \cap \bar{B} \cap \bar{C} \cap \bar{D}) \\ = 1 - P (\bar{A}) P (\bar{B}) P (\bar{C}) P (\bar{D}) \\ = 1 - [(1 - \frac{1}{2}) (1 - \frac{1}{3}) (1 - \frac{1}{4}) (1 - \frac{1}{8})] \Rightarrow 1 - \frac{7}{32} = \frac{25}{32} \end{array}$

Solution:

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