E A multiplechoice test has five questions each with four an

E. A multiple-choice test has five questions, each with four answer choices. Only one of the choices is correct. You randomly guess the answer to each question. What is the probability you do not answer a single question correctly? (That is, that you miss every question.)

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 = 0 ) = ( 5 0 ) * ( 0.25^0) * ( 1 - 0.25 )^5
= 0.2373