The probability of winning on a slot machine is 6 If a perso

The probability of winning on a slot machine is 6%. If a person plays the machine 500 times, find the probability of winning 32 times.

Please show all work, thank you.

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 = 32 ) = ( 500 32 ) * ( 0.06^32) * ( 1 - 0.06 )^468
= 0.0678