Question

For this question, you need at least 6 decimal places.
An exact answer (fractions) is recommended on both parts, especially the first part since it will be used for the second question.

Baumgartner, Prosser, and Crowell are grading 19

calculus exams on which there is a series of 5 multiple choice questions. Each question has 3

answer choices.

Crowell says, "I bet we should expect at least three exams in which no answer is correct if everyone is just guessing."

First, what is the probability that a student gets no answer correct on the 5

multiple choice questions if he or she guesses randomly with no bias? I HAVE THIS FIRST ANSWER


What is the probability that there are at least three exams with no answer correct if all 19

students are guessing?

Hint: use your answer from part (a) as the probability of success here. Your trials are the exams (students) now, and we want at least three successes.

Answer 1

Probability that a student gets no answer correct on the 5 multiple choice questions if he or she guesses randomly with no bias

= = 32/729 = 0.043896

Let X be the number of exams with no answer correct out if the 19 exams

X follows binomial distribution with n = 19 and p = 32/729

The required probability = P(X ≥ 3)

= 1 - P(X < 3)

= 1 - {P(X = 0) + P(X = 1) + P(X = 2)}

= 0.048433