Question

A quiz consists of 20 multiple-choice questions, each with 5 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60 %.

Answer 1

N = 20, the number of questions
p = 1/5 = 0.2, the probability of making a correct guess
q = 1 - p = 0.8, the probability of making an incorrect guess.
Expected success  = 60% or 6 of 10.

From the binomial distribution,
P(6 of 10) = ₁₀C₆ p⁶q⁴
                 = 210*0.2⁶*0.8⁴ = 0.0055

Answer: 0.0055