Question

Section II – During finals week, some instructors tend to use multiple-choice (A, B, C, or D) and true/false questions on the exam. Let us continue working with multiple-choice problems, but let us say instead that the instructor has eight (8) multiple-choice problems with *four possible choices* for each problem. Use this information for all problems on this page!

What are the four requirements for an experiment to be a binomial experiment?

Do the eight multiple-choice questions satisfy those requirements? Explain your answer.

What is the probability of obtaining exactly 5 correct answers?

What is the probability of obtaining at least 5 correct answers?

What is the probability of obtaining at most 6 correct answers?

Answer 1

The four requirements for an experiment to be a binomial experiment :

• number of trials is fixed . in this case n = 8
• There are only two possible outcomes in each trial - a correct answer or a incorrect answer
• The probability of answering each questions correctly does not depend on other questions.
• The probability of correctly answering each question is fixed, one of the four options is correct, so

So, X ~ Binomial( n = 8, p = 0.25)

The probability mass function of X is

Now,

The probability of obtaining exactly 5 correct answers

The probability of obtaining at least 5 correct answers

c) The probability of obtaining at most 6 correct answers