Question

On a multiple-choice examination with three possible answers for each of the five questions. What is the probability that a candidate would get four or more correct answers just by guessing?

Answer 1

Let X = number of correct answers. 

p = probability that a candidate gets a correct answer from three possible answers.

The p.m.f. of X is given by

P(four or more correct answers) = P[X ≥ 4]

= p(4) + p(5)

Hence, the probability of getting four or more correct answers = 11/243.