1.Assume that 11 people, including the husband and wife pair, apply for 4 sales positions. People are hired at random. (1) What is the probability that both the husband and wife are hired? 330 (2) What is the probability that one is hired and one is not? 2. Assume that there are 20 frozen dinners: 9 pasta, 7 chicken, and 4 seafood dinners. The student selects 5 of them. What is the probability that at least 2 of the dinners selected are pasta dinners 3. the bucket containing orange tennis balls and yellow tennis balls from which 5 balls are selected at random, but assume that the bucket contains 7 orange balls and 8 yellow balls. (1) What is the probability that, of the 5 balls selected at random, at least one is orange and at least one is yellow? (2) What is the probability that, of the 5 balls selected at random, at least two are orange and at least two are yellow? 4. Assume that there are 6 different issues of Newsweek magazine, 5 different issues of Time, and 2 different issues of Sports Illustrated, including the December 1st issue, on a rack. You choose 4 of them at random. (1) What is the probability that you choose 3 issues of Newsweek and 1 issue of Time? (2) What is the probability that you choose at least 1 of the Time magazines? 5. Assume that there are 6 different issues of Popular Science magazine, 7 different issues of Time, and 3 different issues of Sports Illustrated, including the December 1st issue, on a rack. You choose 4 of them at random. (1) What is the probability that exactly 3 are issues issue of Popular Science? (2) What is the probability that you choose the December 1st issue of Sports Illustrated? 6. Assume that you randomly select 5 cards from a deck of 52. What is the probability that all of the cards selected are diamonds? 7. You select 10 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)? 8. flipping a fair coin. Assume that the coin is flipped 10 times. What is the probability that both heads and tails occur? 9. An experiment consists of rolling three fair dice --- a red die, a blue die, and a white die --- and recording the number rolled on each die. Assume that the dice are fair, so that all outcomes are equally likely. (1) What probability should be assigned to each outcome? (2) What is the probability that the sum of the numbers rolled is 6? (3) What is the probability that the sum of the numbers rolled is at most 5? 10. Assume that the team plays 6 games. If the team is equally likely to win as to lose each game, what is the probability that they win a string of at least 4 games in a row 11. Assume that 4 digits are selected at random from the set {1,2,3,5,7,9}and are arranged in random order. What is the probability that the resulting 4-digit number is less than 9000? 12. Assume that there are 11 board members: 9 females, and 2 males including Joe. There are 5 tasks to be assigned randomly, including that of notifying members of meeting times. There is at most one task per person. (1) Find the probability that Joe is given a task. (2) Find the probability that Joe is given the task of notifying members of meeting times 13. Assume that there are 15 board members: 10 females, and 5 males including Mark. There are 3 tasks to be assigned. Note that assigning the same people different tasks constitutes a different assignment. (1) Find the probability that both males and females are given a task. (2) Find the probability that Mark and at least one female are given tasks. 14.A \"HAND\"CONSISTS OF A SET OF 5 CARDS SELECTED FROM AN ORDINARY DECK OF 52 CARDS. (1) How many different hands contain exactly 4 diamonds? (2) How many different hands contain cards of exactly one suit