Applications of probability
1. Annie and her friends are playing a game called Doubles. In the game. a player rolls two number cubes at the same time. The outcome of each roll is the sum ofthe two number cubes. Extra points are scored for rolling doubles the same number on both number cubes. Part A: Complete this table to show the sample space for each roll in the game. (a points) Part B: Use Part Ato answer each question. Show your work. Express each probability as a fraction in simplest form. (9 points) a. What is the probability of rolling double sixes? b. What is the probability of rolling doubles? c. What is the probability of rolling a sum of 6 on the two number cubes? d. Annie and Alonzo both roll two number cubes. What is the probability that Annie rolls a sum of 6 and Alonzo rolls doubles? e. On a single roll of two number cubes. are rolling a sum of 6 and rolling doubles mutually exclusive events? f. On a single roll of two number cubes, what is the probability of rolling doubles given that the sum is 6? . , Pmand) A a : Hint. UseF'i | ) P's) . 9. On a single roll of two number cubes. are rolling a sum of 6 and rolling doubles independent events? Explain. DIAGRAMS AND FORMULAS 2. Annie and her friends started a club. The Venn diagram shows information about the 16 members of the club. JUNlORS Bob I'lGnZ' Use the Venn diagram to find each probability. Express each probability as a fraction in simplest terms. Part A: A randomly selected club member is a junior and a girl. (4 points) Part B: A randomly selected club member is not a junior girl. (4 points) Part c: A randomly selected club member is ajunior or a girl. Use the formula pm u .53 = PM) + m5) HA n a. (3 points) Part C: A randomly selected club member is a junior or a girl. Use the formula PM u a) = P01) + rm - RA n a). (3 points) 3. Annie ordered T-shirts for her club to sell at a fundraiser. The table shows the colors and sizes of all the shirts she ordered. Part A: Annie randomly chooses a red shirt. What is the probability that the shirt is large. given that it is red? Show your work. Express your answer as a percent rounded to the nearest tenth. (4 points) Part B: Annie randomly chooses a large shirt. What is the probability that the shirt is red. given that it is large? Show yourwork. Express your answer as a percent rounded to the nearest tenth. (4 points) 4. At a high school movie night, the refreshment stand sells popcorn and soft drinks. 0f the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. 38 students bought both popcorn and a drink. Part A: What is the probability that a student buys a drink? Express your answer as a percent. (2 palms) Part B: What is the probability that a student buys a drink, given that he or she buys popcorn? Express your answer as a percent. rounded to the nearest tenth. (2 points) Part B: What is the probability that a student buys a drink, given that he or she buys popcorn? Express your answer as a percent, rounded to the nearest tenth. (2 points) Part C: Are buying a drink and buying popcorn independent or dependent events? Justify your answer. (2 points) COMBINATIONS AND PERMUTATIONS 5. in a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 ofcers (president, vice president, secretary, and treasurer) and 2 at- Iarge members (who don't have an ofce). Part A: First, the four ofcers are chosen. In how many ways can 4 of the 10 candidates be chosen to be president. vice president. secretary. and treasurer? Is this a combination or a permutation? Explain. (4 points) Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board members. In how many ways can they be chosen? Is this a combination or a permutation? Explain. (4 points) Part c: The chorus decides to choose the 2 atlarge board members from the 6 remaining candidates randomly. What is a fair way to do this? (2 points)
