Assume that a procedure yields a binomial distribution with

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. (USE FORMULA!!!)

n = 5, x = 2, p = 0.70

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 = 2 ) = ( 5 2 ) * ( 0.7^2) * ( 1 - 0.7 )^3
= 0.132