CUET CUET Mathematics 2024 - The probability of a shooter hitting a target is 34. How many minimum number of times must he fire so that the probability of hitting the target at least once is more than 90 \% ? | PYQs + Solutions | AfterBoards
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CUET Mathematics 2024

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Probability

Easy

The probability of a shooter hitting a target is 34\frac34. How many minimum number of times must he fire so that the probability of hitting the target at least once is more than 90%90 \% ?

Correct Option: 2
For n=1n = 1 shot:
Probability of at least one hit =1−= 1 - Probability of missing \newline =1−(0.25)1= 1 - (0.25)¹ \newline =0.75= 0.75
For n=2n = 2 shots: \newline Probability of at least one hit =1−= 1 - Probability of missing all shots \newline =1−(0.25)2= 1 - (0.25)² \newline =1−0.0625= 1 - 0.0625 \newline =0.9375= 0.9375
Since 93.75%>90%93.75\% > 90\%, the minimum number of shots needed is 2.

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