108 Probability of Compound Events


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1 Use any method to find the total number of outcomes in each situation. 6. Nathan has 4 tshirts, 4 pairs of shorts, and 2 pairs of flipflops. Use the Fundamental Counting Principle to find the number of possible outcomes. Nathan has 4 choices of tshirt, 4 choices of shorts, and 2 choices of flipflops = 32 So, the number of possible outcomes is Frozen yogurt is available in 2 sizes and 6 flavors. Use the Fundamental Counting Principle to find the number of possible outcomes. There are 2 choices of sizes and 6 choices of flavors. 2 6 = 12 So, the number of possible outcomes is Malik flips a penny, a nickel, and a dime at the same time. Use the Fundamental Counting Principle to find the number of possible outcomes. There are 2 outcomes from flipping a penny, 2 outcomes from flipping a nickel, and 2 outcomes from flipping a dime = 8 So, the number of possible outcomes is 8. Use any method to find the total number of outcomes in each situation. 9. A pet store has male and female huskies with blue, green, and amber eyes. List each sex. Then pair each sex with each eye color. There are 6 possible outcomes. esolutions Manual  Powered by Cognero Page 1
2 10. A coin is tossed and a 12sided solid with identical faces is rolled. List each outcome from tossing a coin. Then pair each coin outcome with an outcome from rolling a 12sided solid. Coin 12sided Solid head 1 tail 1 head 2 tail 2 head 3 tail 3 head 4 tail 4 head 5 tail 5 head 6 tail 6 head 7 tail 7 head 8 tail 8 head 9 tail 9 head 10 tail 10 head 11 tail 11 head 12 tail 12 There are 24 possible outcomes. esolutions Manual  Powered by Cognero Page 2
3 11. There are 3 truefalse questions on a quiz. List the possible outcomes for Question 1. Pair each outcome for Question 1 with outcomes for Question 2. Match each set of outcomes for Questions 1 and 2 with outcomes for Question 3. There are 8 possible outcomes. 12. Kane rolls a number cube and flips a quarter at the same time. What is the probability he rolls a 1 and the quarter lands heads up? Use the Fundamental Counting Principle to find the number of possible outcomes. There are 6 choices for a number cube and 2 choices for a quarter. 6 2 = 12 There are 12 possible outcomes. Find the probability. There is one way to roll a 1 and flip a head. So, the probability is. 13. A newborn baby is equally likely to be male or female. What is the probability that a mother s first three children will all be girls? Use the Fundamental Counting Principle to find the number of possible outcomes. There are 2 possible outcomes for the first baby, 2 possible outcomes for the second baby, and 2 possible outcomes for the third baby = 8 There are 8 possible outcomes. Find the probability. There is one way to have three girls. So, the probability is. esolutions Manual  Powered by Cognero Page 3
4 14. The table shows the sandwich choices for lunch at a cafe. If a onebread, onemeat, onecheese sandwich is chosen at random, what is the probability that it will be turkey and Swiss on wheat bread? Use the Fundamental Counting Principle to find the number of possible outcomes. There are 3 choices for bread, 4 choices for meat, and 3 choices for cheese = 36 So, the number of possible sandwiches is 36. There is one way to make a sandwich that is turkey and Swiss on wheat bread. So, the probability is. 15. A game requires you to toss a 10sided numbered solid and a 6sided numbered solid to determine how to move on a game board. Find the following probabilities. a. P(same number on both dice) b. P(odd, even) or P(even, odd) a. There are ten outcomes for the 10sided die, and six outcomes for the 6sided die = 60 So, the number of possible outcomes is 60. There are six ways that the toss results in the same number on both dice. They could both be ones, both twos, both threes, both fours, both fives, or both sixes. So, the probability is. b. There are ten outcomes for the 10sided die, and six outcomes for the 6sided die = 60 So, the number of possible outcomes is 60. There are five odd numbers on the 10sided die, and 3 even numbers on the 6sided die. 5 3 = 15 There are 15 ways to get (odd, even). There are five even numbers on the 10sided die, and 3 odd numbers on the 6sided die. 5 3 = 15 There are 15 ways to get (even, odd). Therefore, there are or 30 different ways to (odd, even) or (even, odd). So, the probability is. esolutions Manual  Powered by Cognero Page 4
5 16. Every U.S. citizen has a nine digit social security number. The first three digits are a geographic code, the next two digits are determined by the year and the state where the number is issued, and the last four digits are random numbers. If you are less than 100 years old, what is the probability that the last two numbers are your age? Each of the last two numbers is picked randomly, so there are 10 possibilities for each number = 100 There is only one possibility for your age. So, the probability is. 17. Use Math Tools Each of the spinners shown is spun once. Use a tree diagram to find the following probabilities. a. P(at least one 2) b. P(at least one 3) a. A tree diagram would give the following possible outcomes: 21, 22, 23, 24, 51, 52, 53, 54, 61, 62, 63, and 64. In order to keep the probabilities the same, 61, 62, 63, and 64 must be counted twice. So, there are 16 possible outcomes. There are 7 outcomes where there is at least one 2. So, P(at least one 2) is. b. According to the outcomes in part a, there are 4 outcomes where there is at least one 3. So, P(at least one 3) is. esolutions Manual  Powered by Cognero Page 5
108 Probability of Compound Events
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