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returning each hat before taking out

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by sanju09 » Tue May 24, 2011 1:41 am
A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and returning each hat before taking out the next one?
(A) 1/8
(B) ¼
(C) 3/8
(D) ½
(E) 7/12

[spoiler]Source: Eric's collection on BTG


OA D[/spoiler]
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by Frankenstein » Tue May 24, 2011 4:16 am
Hi,
Total number of ways of picking 4 hats one by one and replacing is 2.2.2.2 = 16
We need exactly 3 red or 3 blue. So, the favorable cases are
BRRR
RBRR
RRBR
RRRB
RBBB
BRBB
BBRB
BBBR (TOTAL 8 CASES)
SO, the probability is 8/16 =1/2

Hence, answer is D

Cheers!
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by iongmat » Tue May 24, 2011 5:34 am
Prob. of 3 r and 1 b is (1/2)^4
But since 1 b can be in any of the 4 positions, prob. = 4*(1/2)^4

Prob. of 3 b and 1 r is (1/2)^4
But since 1 r can be in any of the 4 positions, prob. = 4*(1/2)^4

So, total prob. = 4*(1/2)^4 +4*(1/2)^4 = 1/2
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