A fair coin is flipped 144 times Find the probability that t

A fair coin is flipped 144 times. Find the probability that the coin lands on heads exactly 77 times in the 144 tosses.

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 77 ) = ( 144 77 ) * ( 0.5^77) * ( 1 - 0.5 )^67
= 0.047