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probability problem

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probability problem

by Night reader » Mon Dec 20, 2010 5:41 am
A coin is tossed six times. What is the probability that exactly three heads will show?

(a) 9/16
(b) 1/2
(c) 7/16
(d) 5/16
(e) 3/16

[spoiler]I solved@ # ways three heads = 6C3; eP(3 heads)=P(3 heads)*P(3 tails)= 1/8 * 1/8; P(3 heads in 6 tosses)=20*1/64=5/16[/spoiler]
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by Rahul@gurome » Mon Dec 20, 2010 5:48 am
Another approach based on same logic.

Total number of outcomes = Number of ways to fill 6 places by either H or T = 2^6 = 64

Favorable number of outcomes = Number of ways to fill 6 places by exactly three H's and exactly three T's = 6!/(3!*3!) = 20

Required probability = 20/64 = 5/16

The correct answer is D.
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