The probability that a man can hit a target is 3/4. He tries

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The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target atleast three times, is

1. 291/364
2. 371/464
3. 471/502
4. 459/512
5. None of the above

Correct Option: D

Required Probability
Given, n = 5 and r = 3
Then, Success P = 3/4
Failure, q = 1 - 3/4 = 1/4
Man hit the target thrice
= ⁵c₃ (3/4)³ (1/4)² + ⁵c₄ (3/4)³ (1/4) + ⁵c₃(3/4)⁵
= (270/1024) + (405/1024) + (243/1024)
= 918/1024
= 459/512