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Three gunmen shoot at a target and hit it in an average of 1 for every 4 attempts. If the three gunmen fire simultaneously, what is the probability, in percentage, that the target be hit in 1 attempt?

Based in ITA, a institute from Brazil


The answer is 57.8125.

Murtuza Akhtari by Murtuza Akhtari , 24, India

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1 solution

Mitchell Price
Apr 26, 2014

The probability that all three marksmen miss is given by: ( 3 4 ) 3 s o t h e h i t c h a n c e = 1 − ( 3 4 ) 3 = 37 64 { (\frac { 3 }{ 4 } })^{ 3 }\quad so\quad the\quad hit\quad chance\quad =\quad 1\quad -\quad { (\frac { 3 }{ 4 } })^{ 3 }\quad =\quad \frac { 37 }{ 64 } \quad

so the hit percentage = 57.8125%

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