1. A box of gumdrops was found to contain the number of gumdrops listed in the table. Assume that each gumdrop has an equal chance of being selected. If one gumdrop is drawn from the box: a. What is the probability of drawing an orange gumdrop? b. What is the probability of drawing a lemon or a grape gumdrop? Type Number c. What is the probability of a grape and a cherry gumdrop? Lemon Orange Cherry Grape 2. A pair of fair dice is rolled. a. What is the probability that the two outcomes on a roll sum to 7? o. What is the probability that the outcomes for a roll either a sum to 5 or at least one is a 4 in the pair? 3. The probabilities of events A, B, and AnB are given as P(A) = 2 . P(B) = >, and P(AnB) = ?. Determine the following. a. P(AUB) = =. b. The odds in favor of A occurring, in lowest terms. c. The odds against B, in lowest terms. 4. In order to test a new drug for adverse reactions, the drug was administered to 1,000 test subjects with the following results: 50 subjects reported that their only adverse reaction was a loss ofappetite, 90 subjects reported that their only adverse reaction was a loss of sleep, and 700 subjects reported no adverse reactions at all. a. Create a Venn Diagram for this application. b. If this drug is released for general use, what is the (empirical) probability that a person using the drug will suffer both a loss of appetite and a loss of sleep? 5. How many different license plates are possible if each contains 4 letters (out of the alphabet's 26 letters) followed by 4 digits (from 0 to 9) if no letter can be repeated, but a number can be repeated? 6. Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that: a. Comic D will perform third. b. Comic B will perform second and Comic F will perform third. c. The comedians will perform in the following order: D, B, F, C, E, A. d. Comic E or Comic A will perform first. 7. There are 1 1 candidates for three positions at a restaurant. One position is for a cook. The second position is for a food server. The third position is for a cashier. If all 11 candidates are equally qualified for the three positions, in how many different ways can the three positions be filled? 3. In how many ways can the digits in the number 4,272,727 be arranged? 9. A five-digit number starts with a number between 4-9 in the first position, with no restrictions on the remaining 4 digits. a. Find the probability that a randomly-chosen phone number contains all different digits. b. Find the probability that a randomly-chosen phone number contains at least one repeated digit