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? (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.)
b. Are the outcomes in the sample space equally likely?
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.
e. What happens to 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?