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Three persons P, Q and R independently try to hit a target. If the pro
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28 Jan 2022, 07:22
28 Jan 2022, 07:22
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Question Stats:
44% (01:50) correct
55% (02:06) wrong based on 9 sessions
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Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 3/4, 1/2 and 5/8 respectively, then the probability that the target is hit by P or Q but not by R is
A) 21/64
B) 9/64
C) 15/64
D) 39/64
E) 27/64
A) 21/64
B) 9/64
C) 15/64
D) 39/64
E) 27/64
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Joined: 10 Apr 2015
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Re: Three persons P, Q and R independently try to hit a target. If the pro
[#permalink]
28 Jan 2022, 07:34
28 Jan 2022, 07:34
2
Carcass wrote:
Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 3/4, 1/2 and 5/8 respectively, then the probability that the target is hit by P or Q but not by R is
A) 21/64
B) 9/64
C) 15/64
D) 39/64
E) 27/64
A) 21/64
B) 9/64
C) 15/64
D) 39/64
E) 27/64
If P(person P hits) = 3/4, then P(person P misses) = 1 - 3/4 = 1/4
If P(person Q hits) = 1/2, then P(person P misses) = 1 - 1/2 = 1/2
If P(person R hits) = 5/8, then P(person P misses) = 1 - 5/8 = 3/8
We want to find P(target is hit by P or Q but not by R)
There are three different scenarios that satisfy this:
1) P hits, Q misses, and R misses
2) P misses, Q hits, and R misses
3) P hits, Q hits, and R misses
So, P(target is hit by P or Q but not by R) = P(P hits AND Q misses AND R misses OR P misses AND Q hits AND R misses OR P hits AND Q hits AND R misses)
= P(P hits AND Q misses AND R misses) + P(P misses AND Q hits AND R misses) + P(P hits AND Q hits AND R misses)
= [P(P hits) x P(Q misses) x P(R misses)] + [P(P misses) x P(Q hits) x P(R misses)] + [P(P hits) x P(Q hits) x P(R misses)]
= [3/4 x 1/2 x 3/8] + [1/4 x 1/2 x 3/8] + [3/4 x 1/2 x 3/8)]
= 9/64 + 3/64 + 9/64
= 21/64
Answer: A
gmatclubot
Re: Three persons P, Q and R independently try to hit a target. If the pro [#permalink]
28 Jan 2022, 07:34
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