5.8.4 Test (TS): Applications of Probability Test Archis Chinmulgund Geometry Sem 2 (S3990682) Points possible: 50 Date: ____________ Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work. TABLES AND PROBABILITIES 1. Annie and her friends are playing a dice game called Doubles. In the game, a player rolls two dice at the same time. The outcome of each roll is the sum of the two dice. Extra points are scored for rolling doubles the same number on both dice. Part A: Use the multiplication principle to find the total number of possible outcomes for each roll in the game. (1 point) Part B: Complete this table to show the sample space for each roll in the game. (6 points) 1 2 3 4 5 6 1 2 3 4 5 6 Part C: Use Parts A and B to answer each question. Show your work. Express each probability as a fraction in simplest form. (10 points) a. What is the probability of rolling double sixes? b. What is the probability of rolling doubles? c. Is rolling doubles a simple event or compound event? Explain. d. What is the probability that Annie rolls a sum of 6 and Jos rolls doubles? e. For a single roll of two dice, are rolling a sum of 6 and rolling doubles mutually exclusive events? f. For a single roll of two dice, are rolling a sum of 6 and rolling doubles independent events? Explain. DIAGRAMS AND FORMULAS 2. Annie and her friends started a Doubles Club. The table below shows information about all the members of the club. Boys Girls Juniors 6 8 Seniors 16 12 Part A: Use the table to complete this Venn diagram. (2 points) Part B: Use the Venn diagram in Part A to find each probability when Annie randomly chooses one member of the Doubles Club. Express each probability as a fraction in simplest terms. (9 points) a. Annie chooses a girl who is a junior. b. Annie does not choose a girl who is a junior. c. Annie chooses a girl or a junior. Use the formula . 3. Annie ordered cotton T-shirts for the Doubles Club. The tree diagram below shows the color and sizes of all the shirts she ordered. Part A: Given that Annie chooses a red shirt at random, what is the probability that the shirt will be large? Use the formula . Express your answer as a percent rounded to the nearest tenth. (4 points) Part B: What is the probability that a randomly chosen red shirt will be small? Use the formula . Express your answer as a percent rounded to the nearest tenth. (4 points) 4. Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is: In this problem you will calculate the probability of getting a hand that has exactly two aces in it (A A X). You will do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above. Part A: Use the multiplication principle to tell the total number of three-card hands (permutations) that can be made with two aces. (2 points) Part B: In the answer from Part I, each two-ace hand got counted twice. For example, A as a separate hand from A A A X got counted X. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards? (2 points) Part C: Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction. (2 points) 5. A 2011 study by The National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using cell phones or texting. The data showed that 11% of drivers at any time are using cell phones . Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That's a 5.26% chance per year. Given what you know about probability, determine if cell phone use while driving and traffic accidents are related. Step A: Let DC = event that a randomly selected driver is using a cell phone. What is P(DC)? (1 point) Step B: Let TA = event that a randomly selected driver has a traffic accident. What is P(TA)? Hint: What is the probability on any given day? (1 point) Step C: How can you determine if cell phone use while driving and traffic accidents are related? (1 point) Step D: Given that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation. (1 point) Step E: What is the probability that a randomly selected driver will be distracted by using a cell phone and have an accident? (2 points) Step F: For a randomly selected driver, are the events "driving while using a cell phone" and "having a traffic accident" independent events? Explain your answer. (2 points) Copyright 2016 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use . Any unauthorized copying, reuse, or redistribution is prohibited. Apex Learning and the Apex Learning Logo are registered trademarks of Apex Learning Inc