10-8 Probability of Compound Events

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1 1. Find the number of tennis shoes available if they come in gray or white and are available in sizes 6, 7, or The table shows the options a dealership offers for a model of a car Elisa can take 6 different classes first period, 2 different classes second period, and 3 different classes third period Amber has a denim and a black purse. Ebony has a black, a red, a denim, and a brown purse. Each girl picks a purse at random to bring to the mall. What is the probability the girls will bring the same color purse? 5. A spinner with 8 equal sections labeled 1 8 is spun twice. What is the probability that it will land on 6 after the first spin and on 6 after the second spin? 6. Nathan has 4 t-shirts, 4 pairs of shorts, and 2 pairs of flip-flops Frozen yogurt is available in 2 sizes and 6 flavors Malik flips a penny, a nickel, and a dime at the same time A pet store has male and female huskies with blue, green, and amber eyes A coin is tossed and a 12-sided solid with identical faces is rolled There are 3 true-false questions on a quiz 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? 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? esolutions Manual - Powered by Cognero Page 1

2 14. The table shows the sandwich choices for lunch at a cafe. If a one-bread, one-meat, one-cheese sandwich is chosen at random, what is the probability that it will be turkey and Swiss on wheat bread? 17. Use Math Tools Each of the spinners shown is spun once. Use a tree diagram to find the following probabilities. 15. A game requires you to toss a 10-sided numbered solid and a 6-sided 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. b. 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? a. P(at least one 2) b. P(at least one 3) a. b. 18. Model with Mathematics Give an example of a real-world situation that has 16 outcomes. Sample answer: School sweatshirts come in four sizes and four colors. 19. Find the Error Cameron is finding the number of different outfits he can make with 4 pairs of shoes, 4 pairs of pants, and 5 shirts. Find his mistake and correct it. He should have multiplied rather than added. The correct answer is 80 outfits. 20. Justify Conclusions Marcus has a choice of a white, gray, or black shirt to wear with a choice of tan, black, brown, or denim pants. Without calculating the number of possible outcomes, how many more outfits can he make if he buys a green shirt? Explain your reasoning to a classmate. 4 more outfits; Sample answer: He will have four different pairs of pants that he can wear with that green shirt. esolutions Manual - Powered by Cognero Page 2

3 21. Persevere with Problems Write an algebraic expression for the number of possible outcomes if the spinner is spun x number of times. 24. A bicycle lock has 4 rotating discs and each contains the digits 0 9. How many different lock combinations are possible? F 3024 G 5040 H 6561 J 10, Building on the Essential Question Explain how a tree diagram might be more useful than the Fundamental Counting Principle when finding probability. Sample answer: The Fundamental Counting Principle gives only the total number of outcomes, while a tree diagram makes it easy to see all the possible outcomes when determining a probability. 23. The spinner is spun twice. What is the probability that it will land on 2 after the first spin and on 5 after the second spin? J 25. A restaurant offers a combo special with 3 different sandwiches, 2 different salads, and 5 different drinks. From how many different combos could Keisha choose? A 10 B 11 C 30 D 50 C A B C D A esolutions Manual - Powered by Cognero Page 3

4 26. Short Response Pilan can make outfits of the clothes shown in the table. Draw a tree diagram to show all of the possible outcomes. 29. Use the food data shown in the table. a. What is the median number of fat grams in each sandwich? b. In general, which type of sandwich has a lower amount of fat? Explain. c. Find the measures of variability and any outliers for the data. a. 20; 36 b. Chicken; whereas chicken sandwiches have 8 20 grams of fat, burgers have grams of fat c. Chicken: R: 12; M: 15; Q 1 : 13; Q 3 : 18.5; IR: 5.5; outliers: none; Burgers: R: 26; M: 23; Q 1 : 17; Q 3 : 31.5; IR: 14.5; outliers: none 30. Population density is a unit rate that gives the number of people per square mile. If the area of North Carolina is 48,711 square miles and its population is 8,856,505 people, what is the population density of North Carolina? Round to the nearest tenth people per square mile 27. Sixty-three of the 105 students in the band said that their favorite class was music. Is this sampling representative of the entire school? If so, how many of the 848 students who attend the school would say music is their favorite class? No; this is a biased sample. The students who participate in band are more likely to enjoy music, so more of them may say music is their favorite class, than compared to the entire school population. 28. Maresha took a random sample from a package of jelly beans without looking and found that 30% of the beans were red. Suppose there are 250 jelly beans in the package. How many can she expect to be red? 75 jelly beans Add. 31. (x + 3) + (2x + 4) 3x (9x + 2) + (2x + 9) 11x (3x + 1) + (3x 7) 6x (4x 3) + ( 2x + 2) 2x 1 esolutions Manual - Powered by Cognero Page 4

5 35. ( 4x 2) + ( 5x 1) 9x (3x 8) + ( 10x 2) 7x 10 esolutions Manual - Powered by Cognero Page 5

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