What is the probability of a student passing the exam (grade of 60, 80, or 100) if she guesses the answer for each question?

Question

Suppose that a multiple choice exam has five questions, each of which is worth twenty points and each of which has four possible answers. Suppose that each question has exactly one correct answer listed. What is the probability of a student passing the exam (grade of 60, 80, or 100) if she guesses the answer for each question? Note: guessing the answer means that she chooses one of the four answers with probability 1⁄4 for each question.

Answer 1

This is a binomial distribution B(n,p) with parameters n = 5 and p = 1/4.  The probability of getting exactly k successes in n trials is given by 

 

P(X=k) = _nC_k * p^k * (1-p)^(n-k)  

 

_nC_k is the binomial coefficient n! / (k!(n-k)!) 

 

You need to figure out the probabilities for k = 3, 4 and 5 and add them up