Question

A student guesses at every question of a 5 question multiple choice quiz. Each question has 4 choices, one of which is correct. Calculate the probability of the student passing (achieving a score of 3 or greater) through guessing alone.

Answer 1

P(correct answer) = 1/4 = 0.25

n = 5

This is a binomial distribution

P(X = x) = 5Cx * 0.25^x * (1 - 0.25)^5-x

P(X > 3) = P(X = 3) + P(X = 4) + P(X = 5)

              = 5C3 * 0.25³ * 0.75² + 5C4 * 0.25⁴ * 0.75¹ + 5C5 * 0.25⁵ * 0.75⁰

              = 0.1035