Among 2126 year olds 34 have said they have called a talk sh

Among 21-26 year olds, 34% have said they have called a talk show while under the influence of alcohol. Suppose seven 21-26 year olds are selected at random.

A. What is the probability that at least one has not called a called a talk show under the influence of alcohol? (round to four decimal points as needed)

B. What is the probability that at least one has called a talk show under the infulence of alcohol? (round to four decimal points as needed)

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

a)
P( X < 1) = P(X=0)   
= ( 7 0 ) * 0.34^0 * ( 1- 0.34 ) ^7 +
= 0.0546

b)
P( X > = 1 ) = 1 - P( X < 1) = 0.9454