A student takes a 7 question multiplechoice quiz with 4 choi

A student takes a 7 question multiple-choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 3 questions correct?

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 = 3 ) = ( 7 3 ) * ( 0.25^3) * ( 1 - 0.25 )^4
= 0.173