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Question

A quiz consists of 10 multiple-choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 40 %

P(pass)

Answer 1

We will use the binomial probability formula. If you have access to a binomial distribution probability calculator, you can put in the given numbers and find the probability based on what the problem is asking for.

If we want to get a passing score of 40%, then we need to answer at least 4 questions on the quiz. Each question has 6 possible answers. The success probability is 1/6.

P(X = x) = n! / [x!*(n-x)!] p^x * (1-p)^n-x

P(X ≥ 4) = 1 - P(X < 4) = 1 - 0.9302 = 0.0698

The probability of passing the quiz with a minimum of 40% is about 0.0698.