Question

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

Answer 1

$P(A)=\frac{100-55}{100}=\frac{45}{100}=\frac{9}{20}$

Answer 2

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.