In a group of ten students each student has a probability of

In a group of ten students, each student has a probability of 0.7 of passing an exam. What is the probability that exactly 7 of them will pass an exam?

(a) 0.9829

(b) 0.2668

(c) 0.0480

(d) 0.9520

Show work please so i can learn how to do it, thankyou

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 = 7 ) = ( 10 7 ) * ( 0.7^7) * ( 1 - 0.7 )^3
= 0.2668