# GMAT® Practice : Probability

Concept: Probability of complementary and exhaustive events.

This GMAT practice question is a Probability question and is a problem solving question. The question is a typical example of how it makes sense to first find the probability of the event complementary to the event asked and then compute the required probability.

#### Question: 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?

1. 1
2. $\frac{1}{256}\\$
3. $\frac{81}{256}\\$
4. $\frac{175}{256}\\$
5. $\frac{144}{256}\\$

#### Find the probability of the complement

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

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

The event of not hitting the target even once is the complement of the event of hitting the target at least once.

The probability that he will not hit the target in any given shot = 1 - $\frac{1}{4}\\$ = $\frac{3}{4}\\$

Therefore, the probability that he will not hit the target in any of the four shots = $\frac{3}{4}\\$ * $\frac{3}{4}\\$ * $\frac{3}{4}\\$ * $\frac{3}{4}\\$ = $\frac{81}{256}\\$

#### Find the probability of the required event

The probability that he will hit the target at least in one of the four shots = 1 - {probability of not hitting the target even once}

= 1 - $\frac{81}{256}\\$ = $\frac{175}{256}\\$

Choice D is the correct answer.

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