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Question: The probability that a man can hit a target is ¾. He tries 5 times. The probability that he will hit...

The probability that a man can hit a target is ¾. He tries 5 times. The probability that he will hit the target at

least three times is

A

291/364

B

371/464

C

471/502

D

459/512

Answer

459/512

Explanation

Solution

We have p = 34\frac{3}{4} ⇒ q = 14\frac{1}{4} and n = 5.

Therefore required probability

= 5C3(34)3(14)2+5C4(34)(14)+5C5(34)55C_{3}\left( \frac{3}{4} \right)^{3}\left( \frac{1}{4} \right)^{2} +^{5}C_{4}\left( \frac{3}{4} \right)^{}\left( \frac{1}{4} \right) +^{5}C_{5}\left( \frac{3}{4} \right)^{5}

= 10.2745+5.8145+24345=270+405+2431024=459512\frac{10.27}{4^{5}} + \frac{5.81}{4^{5}} + \frac{243}{4^{5}} = \frac{270 + 405 + 243}{1024} = \frac{459}{512}