Question

Suppose you are taking an exam that only includes 80 multiple choice questions. Each question has five possible choices and only one of them is correct answer per question. Questions are not related to the material you know, so you guess the answer randomly in the order of questions written and independently. The probability that less than five questions are needed to mark the three correct answers is

Answer 1

Given that each question has 5 options and only 1 of them is correct so probability of selecting the correct answer is 1/5

So probability of success, p=1/5

Now to find the probability that less than 5 questions are needed to mark the three correct answers.

to mark 3 correct answers one has to answer minimum 3 questions and all of them should be correct or one can answer 4 questions and 3 out of them should be correct, only these two cases are applicable because of the constraint of less than 5 questions.

So probability is given by

P(all 3 attempted are correct)+P(3 out of 4 attempted are correct)

Hence the probability is 21/625.