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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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The probability of a man hitting a target is $ \large\frac{3}{4}$. He tries 5 times. The probability that the target will be hit at least 3 times is

$\begin {array} {1 1} (A)\;\large\frac{291}{364} & \quad (B)\;\large\frac{371}{464} \\ (C)\;\large\frac{471}{502} & \quad (D)\;\large\frac{459}{512} \end {array}$


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Using binomial distribution we have to find $ P(3) +P(4)+P(5)$
This probability is
$ 5C_3 \bigg( \large\frac{3}{4} \bigg)^3\bigg( \large\frac{1}{4} \bigg)^2+5C_4\bigg( \large\frac{3}{4} \bigg)^4\bigg( \large\frac{1}{4} \bigg)^1+5C_5\bigg( \large\frac{3}{4} \bigg)^5\bigg( \large\frac{1}{4} \bigg)^0$
$= \large\frac{270+405+243}{45} = \large\frac{918}{1024}$
$ = \large\frac{459}{512}$
Ans : (D)
answered Jan 3, 2014 by thanvigandhi_1

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