Probability Answers

Quant/Math - CAT 2008

CAT Sample Questions - Question 4 the day : April 20, 2004

The question for the day is from the topic 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?

 

(1)	1		(2)	1/256
(3)	81/256		(4)	175/256

 

Correct choice - (4) Correct Answer -( 175/256 )
 

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Explanatory Answer

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 of he will hit hit target in exact one shot
Therefore, the probability that he will not hit the target in all the four shots =3/4  *  3/4  *  3/4  *  3/4  = 81/256 

Hence, the probability that he will hit the target at least in one of the four shots =
1 -  81/256
 

= 175/256 .