A fair coin is tossed 100 times. What is the probability that more than 55 heads are observed?

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17-08-2014
Mathematics

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A fair coin is tossed 100 times. What is the probability that more than 55 heads are observed?

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Everest2017 Everest2017 · Answer 1 · 2014-08-17T05:42:01-04:00

Let us say T= probability of head turning up = 1/2 in one toss
H = probability of a tail turning up = 1/2 in one toss

Then P (56 heads or more) =
   1/2^100 [ C(100,56) + C(100,57) + C(100,58) + ....
       C(100,98) + C(100,99) + C(100,100) ]

   where C(N, R) = N ! / [ (N - R)! R! ] number of occurrances of R formed from
   N tosses.

konrad509 konrad509 · Answer 2 · 2014-08-17T05:54:49-04:00

konrad509 konrad509

17-08-2014

[tex]P(A)=\frac{100-55}{100}=\frac{45}{100}=\frac{9}{20}[/tex]

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