Two students taking a multiple choice exam with 20 questions and four choices for each question have the same incorrect answer on seven of eight incorrectly answered 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, the guess for one problem is independent of the guess for the other problems. The probability of getting agreement on seven or more out of eight questions is:
A)0.9996.
B)0.0004.
C)0.25.
D)None of the answer options is correct.

Question

Quizplus · Accepted Answer

The probability that student A and student B both guess the same incorrect answer for a particular question is 1/4. Therefore, the probability that they both guess different answers is 1 - 1/4 = 3/4. Since there are 20 questions, the probability that they have agreement on 7 or more questions is:

${20 \choose 7} (1/4)^7 (3/4)^{13} + {20 \choose 8} (1/4)^8 (3/4)^{12}$

This can be computed using a binomial distribution or a calculator to get approximately 0.0004.

Two Students Taking a Multiple Choice Exam with 20 Questions