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# Three archers each have an equal chance of hitting a target, and if on

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Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
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Kudos [?]: 782 [0], given: 22

Three archers each have an equal chance of hitting a target, and if on [#permalink]

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08 Nov 2010, 03:51
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Difficulty:

25% (medium)

Question Stats:

67% (01:50) correct 33% (01:03) wrong based on 27 sessions

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Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target?

(A) 1/27
(B) 16/81
(C) 8/27
(D) 19/27
(E) 26/27
[Reveal] Spoiler: OA

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Re: Three archers each have an equal chance of hitting a target, and if on [#permalink]

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08 Nov 2010, 04:14
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rxs0005 wrote:
Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target?

(A) 1/27
(B) 16/81
(C) 8/27
(D) 19/27
(E) 26/27

Let the probability of an archer hitting a target be $$x$$. Then the probability of two hitting the target will be $$P=x*x=\frac{4}{9}$$ --> $$x=\frac{2}{3}$$, so the probability of an archer missing the target will be $$P=1-\frac{2}{3}=\frac{1}{3}$$.

The probability of all three men missing the target will be $$P=(\frac{1}{3})^3=\frac{1}{27}$$.

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Re: Three archers each have an equal chance of hitting a target, and if on [#permalink]

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30 Aug 2016, 18:57
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Re: Three archers each have an equal chance of hitting a target, and if on   [#permalink] 30 Aug 2016, 18:57
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