The computers of six faculty members in a certain department 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). a?. ?What is the probability that both selected setups are for laptop computers? b?. ?What is the probability that both selected setups are desktop machines? c?. ?What is the probability that at least one selected setup is for a desktop computer? d?. ?What is the probability that at least one computer of each type is chosen for setup?

Solution: a) Step 1 : Here it is given that among 6 faculty members who want to replace their computers. two of the faculties selected laptop machines and other four have chosen desktop machine. Since only two of the setup can be done in a day. The possible outcomes will be (1,2), (1,3) ,and so on ( computers are numbered from 1 to 6) Step 2 : If we consider the numbers 1 and 2 as the laptop machines and the remaining as the desktop machines what they chosen. Then among the 15 possible outcomes, the possible outcome that both selected setups are laptop computers will be (1,2) Step 3: So the probability that selected setups are laptop machines will be 1/15 (only one way among 15 possible outcomes) b) step 1: Among the 15 possible outcomes, the outcome that both selected setups are desktop computers will be 1) (3,4) 4) (4,5) 2) (3,5) 5) (4,6) 3) (3,6) 6) (5,6) Step 2 : So the probability that both selected setups are desktop machines is = 6/15 c) Step 1 : The possible outcomes that at least one selected setup is for a desktop computer 1) (2,3) 5) (3,4) 9) (4,6) 2) (2,4) 6) (3,5) 10) (5,6) 3) (2,5) 7) (3,6) 4) (2,6) 8) (4,5) Step 2 : So the probability that at least one selected setup is for a desktop computer = 10/15 d) tep 1: The possible outcomes that at least one computer of each type is chosen for set up 1) (1,3) 5) (2,3) 2) (1,4) 6) (2,4) 3) (1,5) 7) (2,5) 4) (1,6) 6) (2,6)