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# In a department store prize box, 40% of the notes give...

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Joined: 06 Sep 2013
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In a department store prize box, 40% of the notes give... [#permalink]  18 Sep 2013, 11:31
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Difficulty:

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Question Stats:

63% (03:04) correct 38% (02:27) wrong based on 48 sessions
In a department store prize box, 40% of the notes give the winner a dreamy vacation; the other notes are blank. What is the approximate probability that 3 out of 5 people that draw the notes one after the other, and immediately return their note into the box get a dreamy vacation?

a) 0.12
b) 0.23
c) 0.35
d) 0.45
e) 0.65
[Reveal] Spoiler: OA
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Re: In a department store prize box, 40% of the notes give... [#permalink]  18 Sep 2013, 11:39
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jlgdr wrote:
In a department store prize box, 40% of the notes give the winner a dreamy vacation; the other notes are blank. What is the approximate probability that 3 out of 5 people that draw the notes one after the other, and immediately return their note into the box get a dreamy vacation?

a) 0.12
b) 0.23
c) 0.35
d) 0.45
e) 0.65

The probability of winning is 40% = 40/100 = 2/5.
The probability of NOT winning is 60% = 3/5.

$$P(WWWNN)=\frac{5!}{3!2!}*(\frac{2}{5})^3*(\frac{3}{5})^2=\frac{144}{625}\approx{23}$$ (we multiply by $$\frac{5!}{3!2!}$$, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is $$\frac{5!}{3!2!}$$).

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Re: In a department store prize box, 40% of the notes give... [#permalink]  21 Nov 2014, 10:04
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Re: In a department store prize box, 40% of the notes give...   [#permalink] 21 Nov 2014, 10:04
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