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P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw

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Bunuel
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P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw [#permalink] New post   26 Nov 2018, 02:40
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P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, twice in 3 shots,. They fire simultaneously. What is the probability that at least 2 shots hit?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6
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E
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Re: P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw [#permalink] New post   26 Nov 2018, 03:07
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P (hitting the target) = \(\frac{4}{5}\)
P (not hitting the target) = \(\frac{1}{5}\)

Q (hitting the target) = \(\frac{3}{4}\)
Q (not hitting the target) = \(\frac{1}{4}\)

R (hitting the target) =\(\frac{2}{3}\)
R (not hitting the target) =\(\frac{1}{3}\)

Required probability is \(PQ\overline{R}\) + \(P\overline{Q}R\) + \(\overline{P}QR\) + \(PQR\)

= \(\frac{1}{5} + \frac{1}{10} + \frac{2}{15} + \frac{2}{5}\)

= \(\frac{5}{6}\)

OPTION: E
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Re: P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw [#permalink] New post   26 Nov 2018, 17:54
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Bunuel wrote:
P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, twice in 3 shots,. They fire simultaneously. What is the probability that at least 2 shots hit?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6



P of P hit= 4/5 P miss 1/5
P of Q hit = 3/4 , miss 1/4
P of R hit 2/3 , miss 1/3

P of atleast 2 hits
(4/5*3/4*1/3)+(4/5*1/4*2/3)+(1/5*3/4*2/3)+(4/5+3/4+2/3)

Solve we get option E ;5/6
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Re: P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw [#permalink] New post   17 Jul 2020, 04:11
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Bunuel wrote:
P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, twice in 3 shots,. They fire simultaneously. What is the probability that at least 2 shots hit?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6


This is not how probability questions are worded -- if we say something like "a car can drive 80 miles in one hour", we're describing a maximum, not a probability.

Assuming the question is expressing probabilities, each individual probability is so high that only answers D and E are even remotely plausible. You can avoid working out all the cases here just by asking "what is the probability that P and one other shooter hits the target?" That probability alone is higher than 2/3, so E must be right.
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Re: P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw [#permalink] New post   15 Nov 2023, 14:46
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Re: P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw [#permalink]
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