Two Students Taking a Multiple Choice Exam with 20 Questions

Multiple Choice

Two students taking a multiple choice exam with 20 questions and four choices for each question have the same incorrect answer on eight of the problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is:

A) a binomial distribution with n = 8 and p = 0.25.
B) a binomial distribution with n = 20 and p = 0.4.
C) a Normal distribution with  = 8 and  = 0.25.
D) a Normal distribution with  = 20 and  = 0.4.