The probability of a man hitting a target is 1/4. How many times must he
fire so that the probability of his hitting the target at least once is greater
than 2/3?
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Asked on November 22, 2019 by
Shravan Pawar
The probability of a man hitting a target is 1/4. How many times must he fire so that the probability of his hitting the target at least once is greater than 2/3 ?
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Suppose the man fires n times and let X denote the number of times he hits the target. Then,
P(X=r)=n
C
r
(
4
1
)
r
(
4
3
)
n−r
,r=0,1,2,..,n
It is given that
P(X≥1)>
3
2
1−P(X=0)>
3
2
1−n
C
0
(
4
1
)
0
(
4
3
)
n
>
3
2
1−(
4
3
)
n
>
3
2
(
4
3
)
n
<
3
1
⟹n=4,5,6,..
Hence, the man must fire at least 4 times.
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Answer:
The probability of a man hitting a target is 1/4.
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