Question

Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 5 questions, find the probability that he will answer at least 4 questions correctly. Round your answer to the nearest thousandth.

Answer 1

Solution: Let X be the number of questions Richard gets correct.

Then X follows binomial distribution with and

Where:

is the total number of questions

is the probability of correct answer.

We are required to find the probability that he will answer at least 4 questions correctly.

Mathematically we have to find:

We know the binomial probability model is:

Therefore, the probability that he will answer at least 4 questions correctly is .