e. Are the probabilities you found in parts (a)-(f) experimental probabilities or theoretical probabilities? Explain.
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1 1. Josh is playing golf. He has 3 white golf balls, 4 yellow golf balls, and 1 red golf ball in his golf bag. At the first hole, he randomly draws a ball from his bag. a. What is the probability he draws a white golf ball? b. What is the probability he draws a red golf ball? c. What is the probability he draws a yellow golf ball? d. On the sixth hole, Josh drives one of his white golf balls into a pond and has to draw another ball from his bag. What is the probability he draws a white golf ball? e. What is the probability he draws a red golf ball? f. What is the probability he draws a yellow golf ball? e. Are the probabilities you found in parts (a)-(f) experimental probabilities or theoretical probabilities? Explain. 2. To help his 3-year-old sister Emily learn her colors, Kyle has put some yellow, green, red, and blue blocks in a bucket. Emily draws a block from the bucket, names its color, and puts the block back in the bucket. Then Kyle mixes the blocks, and Emily draws again. In playing this game 20 times, Emily draws a yellow block 6 times, a green block 2 times, a red block 8 times and a blue block 4 times. a. Based on Emily s draws, what is the probability of drawing a yellow block from the bucket? b. What is the probability of drawing a green block from the bucket? c. What is the probability of drawing a red block from the bucket? d. What is the probability of drawing a blue block from the bucket? e. Are the probabilities you found in parts (a)-(d) experimental probabilities or theoretical probabilities? Explain. f. There are a total of 10 blocks in the bucket. Based on the results of Emily s 20 draws, how many yellow, green, red, and blue blocks would you expect to be in the bucket? Explain. Yellow: Red: Green: Blue:
2 3. A pyramid has four faces that are congruent equilateral triangles. The faces of a game piece that is a pyramid are labeled with the numbers 1, 2, 3, and 4. A roll of the game piece is determined by the number on the face the game piece lands on. Below are the rules of a game played with two of such game pieces. Player I and Player II take turns rolling two 4-sided number cubes. If the sum of the numbers rolled is odd, Player I gets a point. If the sum of the numbers rolled is even, Player II gets a point. The player with the most points after 32 rolls wins. a. Make a tree diagram that shows all of the possible outcomes of rolling two 4-sided number cubes. b. What is the probability of rolling a sum of 5? c. What is the probability of rolling a sum of 4? d. What is the probability of rolling a sum of 7? e. Do you think the game is fair? Explain. 4. There are five blue marbles, seven orange marbles, and eight yellow marbles in a bag. You draw one marble. Find each probability. a. P(blue marble) b. P(yellow marble) c. P(orange marble) d. If you double the number of blue, orange, and yellow marbles will the probabilities of draw each color marble change? Explain. e. How many yellow marbles would you add to the original bag so that half of the marbles are yellow? f. What marbles could you add or remove to the original bag so the probability of drawing a orange marble is 1 3?
3 5. A bag of skittles contains yellow, orange, green, red and purple skittles. The probability of picking a yellow or orange skittle is 1. 8 The probability of picking a green or red skittle is 1. 4 a. What is the probability of picking a purple skittle? b. If there are 72 skittles in a pack how many are yellow, orange, green, red and purple? 6. A bag has green, yellow, and blue blocks in it. 2 of the blocks are green. 1 of the blocks are yellow. 5 3 a. What is the probability of choosing a blue block? b. If there are 30 blocks in the bag how many of the blocks will be green? Yellow? Blue? 7. Today, the school s cafeteria is offering a choice of pizza or spaghetti. You can get milk or juice to drink. For dessert you can get pudding or an apple. You must take one of each choice. Draw a tree diagram to show all possible lunches. 8. A clothing store sells shirts in three sizes: small, medium, and large. The shirts come with buttons or with snaps. The colors available are blue or beige. Draw a tree diagram to show all possible shirt size and color outcomes.
4 9. Shawn has a spinner that is divided into four regions. He spins the spinner several times and records his results in a table. Region Number of Times Spinner Lands in Region a. Based on Shawn s results, what is the probability of the spinner landing on region 1? b. What is the probability of the spinner landing on region 2? c. What is the probability of the spinner landing on region 3? d. What is the probability of the spinner landing on region 4? e. Make a drawing of what Shawn s spinner might look like. 10. When green and red are combined they produce brown. Spinning the two spinners below will result in brown when one spinner lands on green and the other lands on red. a. What is the probability that brown will be made if each spinner is spun once?
5 11. Kaleb has created a game called Making Orange. To play the game, a player spins twice. If the player gets yellow in one section and red in the other, the player wins, because yellow and red together make orange. The player can choose either spinner for either of their two spins. a. Kaleb spins each spinner once. What is the probability he will make orange? b. If you only played the game with the first spinner what would the probability of making orange be? c. If you only played the game with the second spinner what would the probability of making orange be? d. What combination of spinners are you most likely to make orange with? Both? Just the first? Just the second? Explain.
6 12. The dinner at a party consists of a main course and a desert. Each combination is equally likely to be given to a guest. Main Course Steak Chicken Parmesan Lobster Tofu Hamburger a. Show how you can find the total possible outcomes for a meal. Dessert Pudding Cake Ice Cream Candy Bar b. If meals are made randomly what is the theoretical probability that a meal will include lobster? c. If meals are made randomly, what is the theoretical probability of a meal having tofu and ice cream? 13. In a game, two players take turns rolling two number cubes, each numbered 1 to 6. The numbers are added, and the sum is multiplied by 6. If the final result is an odd number, Player I gets 1 point. If the final result is an even number, Player II gets 1 point. a. List all the possible outcomes of a turn (that is, list the final results when the sum of two number cubes is multiplied by 6). b. What is the probability the final number will be odd? What is the probability that the final number will be even? Is this a fair game?
7 14. How does collecting more data help you predict the outcome of a situation? 15. How do you determine the experiment probability? 16. How can you determine whether the outcomes of a probability event are all equally likely, and why would this information matter? 17. How does the experimental probability compare to theoretical probability for a given situation? 18. How can you decide whether a game is fair or not? 19. How do you determine probability using a spinner? 20. When using a tool (coin, number cube, spinner, deck of cards) to simulate a fair game, what things must you consider? 21. How does understanding probability help you design a winning strategy? 22. How can an area model represent a situation to help analyze probabilities?
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