## Passing an Exam on Pure Luck

A multiple choice exam has 40 questions, all multiple choice. Each question contains 4 options, of which one gets full marks, and the other three get no marks. The pass mark is 24 out of 40,

If the correct answers are randomly distributed amongst the four options, and the student guesses randomly, they will guess correctly one quarter of the time. We can model the student's score by a binomial distribution

\[B(40,0.25)\]

.,We calculate

\[P(X \ge 24)=1-P(X \le 23) =1-0.99999717=0.00000283\]

.Highly unlikely.