Question

A multiple choice test has 10 questions. Each question has four answer choices.

a. What is the probability a student randomly guesses the answers and gets exactly six questions correct?
b. Is getting exactly 10 questions correct the same probability as getting exactly zero correct? Explain.
c. Describe the steps needed to calculate the probability of getting at least six questions correct if the student randomly guesses.

Answer 1

This is a binomial Probability Distribution
a.
p(getting 6 right) = 10C6 (1/4)^6 (3/4)^(10-6) = 0.162 or 1.62%

b P( 10 right) = (1/4)^10
P ( 0 right) = (3/4)^10 so they are not the same

c. P(at least 6 correct ) = P(6) + P(7) + P(8) + P(9) + P(10)