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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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Math Expert
Joined: 02 Sep 2009
Posts: 55228
P can hit a target 4 times in 5 shots, Q, 3 times in 4 shots and R, tw  [#permalink]

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26 Nov 2018, 02:40
00:00

Difficulty:

35% (medium)

Question Stats:

70% (02:17) correct 30% (02:46) wrong based on 46 sessions

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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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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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26 Nov 2018, 03:07
3
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]

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26 Nov 2018, 17:54
1
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] 26 Nov 2018, 17:54
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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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