A random variable X counts the number of successes in 20 ind

A random variable X counts the number of successes in 20 independent trials. The probability that any one trial is unsuccessful is 0.42. What is the probability of exactly eight successful trials?

(a) 0.17

(b) 0.05

(c) 0.52

(d) 0.08

(e) 0.42

(f) None of the above

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 = 1 - 0.42 = 0.58
P( X = 8 ) = ( 20 8 ) * ( 0.58^8) * ( 1 - 0.58 )^12
= 0.0486 ~ 0.05