1. The computers of six faculty members in a certain depart- ment are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2, . . . , 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).
2. What is the probability that both selected setups are for laptop computers?
3. What is the probability that both selected setups are desktop machines?
4. What is the probability that at least one selected setup is for a desktop computer?
5. What is the probability that at least one computer of each type is chosen for setup?

The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 40% of all purchasers request A, 55% request B, 70% request C, 63% request A or B, 77% request A or C, 80% request B or C, and 85% request A or B or C, determine the probabilities of the following events. [Hint: A or B is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.]

1. The next purchaser will request at least one of the three options.
2. The next purchaser will select none of the three options.
3. The next purchaser will request only an automatic trans-
4. mission and not either of the other two options.
5. The next purchaser will select exactly one of these three