Consider a fair coin What is the probability of obtaining at

Consider a fair coin.

What is the probability of obtaining at least 4 head if a fair coin is flipped 17 times?

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 < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 17 3 ) * 0.5^3 * ( 1- 0.5 ) ^14 + ( 17 2 ) * 0.5^2 * ( 1- 0.5 ) ^15 + ( 17 1 ) * 0.5^1 * ( 1- 0.5 ) ^16 + ( 17 0 ) * 0.5^0 * ( 1- 0.5 ) ^17   
= 0.006
P( X > = 4 ) = 1 - P( X < 4) = 0.994