Aptitude Discussion

Q. |
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? |

✖ A. |
1 |

✖ B. |
1/256 |

✖ C. |
81/256 |

✔ D. |
175/256 |

**Solution:**

Option(**D**) is correct

The man will hit the target even if he hits it once or twice or thrice or all four times in the four shots that he takes.

So, the only case where the man will not hit the target is when he fails to hit the target even in one of the four shots that he takes.

The probability that he will not hit the target in one shot =1 - Probability that he will hit target in exact one shot

$=1-\dfrac{1}{4}$

$=\dfrac{3}{4}$

Therefore, the probability that he will not hit the target in all the four shots

\(=\left(\dfrac{3}{4}\right)\times\left(\dfrac{3}{4}\right)\times \left(\dfrac{3}{4}\right)\times\left(\dfrac{3}{4}\right)\)

\(=\dfrac{81}{256}\)

Hence, the probability that he will hit the target at least in one of the four shots:

\(=\left(1-\dfrac{81}{256}\right)\)

\(=\dfrac{175}{256}\)

**Anu**

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Because we can not form the structure in the way you have created. You are taking 1 hit in four shots for four times (16 shots). That is not a valid approach.

**Vaibhav**

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As said he can hit target once in four shot but not necessarily he hits that's why probability is not 100%

This is only a probability that he CAN hit the target once in four shots. It's not that he WILL hit the target in one of the four shots.

**Alicia**

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My thought would have been $1/4*1/4*1/4*1/4=1/256$

Probability is not my strong suit, therefore I am sort of confused as to why it isn't 1/256

**VeeraraghavanK**

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It looks apparently that the answer is 1/4 since he fires 4 shots. The question could have been : "probability that the target is fired at least once"

Is there any other alternate method

Hi , if we consider the cases where he hits , it could be

HMMM+MHMM+MMHM+MMMH

But the above isnt giving me the right answer , why so ?