A group of 30 students from a school is part of the audience

A group of 30 students from a school is part of the audience for a TV game show. The total number of people in the audience is 140. What is the theoretical probability of 4 students from the school being selected as contestants out of 8 possible contestant spots?

P(4 students selected) = ? Round to three decimal places 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

P( Success on selecting a person out of 140) = 30/140 = 0.2143

P( X = 4 ) = ( 8 4 ) * ( 0.2143^4) * ( 1 - 0.2143 )^4
= 0.056