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  4. The probability that a man can hit a target is (3/4), he tries 5 times. The probability that he will hit the target at least three times is

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Q. The probability that a man can hit a target is $\frac{3}{4},$ he tries $5$ times. The probability that he will hit the target at least three times is

NTA AbhyasNTA Abhyas 2022

Solution:

$p=\frac{3}{4},q=\frac{1}{4},n=5$
Probability $={}^{5}C_{3}^{}\left(\frac{3}{4}\right)^{3}\left(\frac{1}{4}\right)^{2}+{}^{5}C_{4}^{}\left(\frac{3}{4}\right)^{4}\left(\frac{1}{4}\right)+{}^{5}C_{5}^{}\left(\frac{3}{4}\right)^{5}=\frac{459}{512}$