Consider a binomial probability distribution with p 065 and

Consider a binomial probability distribution with p = 0.65 and n = 6. Determine the probability: P(x 1)

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 < = 1) = P(X=1) + P(X=0)   
= ( 6 1 ) * 0.65^1 * ( 1- 0.65 ) ^5 + ( 6 0 ) * 0.65^0 * ( 1- 0.65 ) ^6
= 0.022