Question

A multiple-choice test consists of 7 questions. Each question has answer choices of a, b, c, and d, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that he gets fewer than 2 of them correct?

Answer 1

Total number of multiple-choice questions in a test : n=7

Number of choices for each question =4

Only one of the choices is correct;

If a student randomly guesses, Probability of answering a question correctly : p = 1/4 =0.25

X : Number of questions the students gets correct.

X follows binomial distribution with n=7 and p=0.25(q=1-p=0.75)

Probability mass function of X is given by:

Probability of getting 'r' questions correct = P(X=r)

probability that he gets fewer than 2 of them correct = P(X<2) = [P(X=0)+P(X=1)]

P(X<2) = [P(X=0)+P(X=1)] = 0.1335+0.3115=0.4450

probability that he gets fewer than 2 of them correct = 0.4450