A professor assigns five problems to be completed as homework. At the next class meeting, two of the five
problems will be selected at random and collected for grading. You have only completed the first three
problems.

(a) What is the sample space for the chance experiment of selecting two problems at random? (Hint: You
can think of the problems as being labeled A, B, C, D, and E. One possible selection of two problems
is A and B. If these two problems are selected and you did problems A, B, and C, you will be able to
turn in both problems. There are nine other possible selections to consider.) (Enter your answers in
the form AB. Enter your answers as a comma-separated list.)

(b) Are the outcomes in the sample space equally likely?
Yes
No

(c) What is the probability that you will be able to turn in both of the problems selected?

(d) Does the probability that you will be able to turn in both problems change if you had completed the
last three problems instead of the first three problems? Explain.

Yes, the probability does not change. The problems are being selected at random, and each
problem is equally likely.
Yes, the probability does not change. The problems are being selected at random, and each
problem is not equally likely.
No, the probability does not change. The problems are being selected at random, and each
problem is equally likely.
No, the probability does not change. The problems are being selected at random, and each
problem is not equally likely

(e) What is the probability that you will be able to turn in both problems selected if you had completed
four of the problems rather than just three?