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tossed six times

by sanju09 » Fri Mar 18, 2011 2:32 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



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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Mar 18, 2011 5:35 am
Each of the toss has a probability of 1/2 for head and 1/2 for tail.
Probability of 3 tails and then 3 heads (TTTHHH) = (1/2)^6 = 1/64
There will be other combinations also where there will be exactly 3 heads.
Number of ways of getting exactly 3 heads = 6C3 = 20
Therefore, probability that exactly three heads will show = 20/64 = 5/16

The correct answer is D.
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