A man can hit a target once in 4 shots If he fires 4 shots in succession what is the probability tha...........

Quantitative Aptitude ( CCS) Probability

A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?

81/256

1/256

175/256

144/256

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Explanation:

You hit the target if you hit it at least once.
Say, if you hit the target on the first shot, you are done no matter what you do on the rest of the 3 shots.
If you do not hit the target on the first shot, but hit it on the second shot, again, you are done after that... etc
Probability of hitting the target = (1/4) + (3/4)*(1/4) + (3/4)*(3/4)*(1/4) + (3/4)*(3/4)*(3/4)*(1/4)
= (1*64 + 3*16 + 9*4 + 27)/256 = 175/256