Answer all questions and show all of your work. 1. Assume CCC disease has a 10% prevalence rate. A company launched XX test method. It's false positive rate is 10% and the true positive rate is 90%. Find the probability that a subject actually has CCC given that he or she has a positive test result. 2. In California's Fantasy 5 lottery game, winning the jackpot requires that you select 4 different numbers from 1 to 39, and the same 4 numbers must be drawn in the lottery. The winning numbers can be drawn in any order, so order does not make a difference. (a) How many different lottery tickets are possible? (b) Find the probability of winning the jackpot when one ticket is purchased. 3. We have a four-digit passcode keypad to get into a house. Each digit can be one of 0, 1, 2, ..., 9. (a) How many different passcodes are possible? (b) Find the probability to unlock the door when one passcode is entered