COMPOUND PROBABILITIES USING LISTS, TREE DIAGRAMS AND TABLES

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1 OMOUN OBBILITIES USING LISTS, TEE IGMS N TBLES LESSON 2-G EXLOE! Each trimester in E a student will play one sport. For first trimester the possible sports are soccer, tennis or golf. For second trimester the possible sports are basketball or volleyball. For third trimester the possible sports are dodgeball or rugby. How many different groups of three sports could a student play? What is the probability a student will be enrolled in tennis, basketball and dodgeball if a schedule is assigned at random? Follow the steps below to answer these questions. THEE SOTS Step 1: One way to organize the three sports a student might play in a year is to make a list of all the possibilities. a. Two combinations are listed below. opy and complete the list. S, B, S, B, b. How many different groups of three sports are possible for a student to be assigned in one year based on your list? How did you find the answer? Step 2: tree diagram is another way to organize the information to determine possible combinations. Each column in the tree diagram represents one of the trimesters. The sports are listed in the columns. eading the chart from left to right shows the different possible groups of sports a student may play. a. opy and complete the tree diagram below. S B V T B G 28 Lesson 2-G ~ ompound robabilities Using Lists, Tree iagrams nd Tables

2 EXLOE! (ONTINUE) Step2: b. How many different groups of three sports are possible for a student to be assigned in one year based on your tree diagram? How did you find the answer? Step 3: table is a third way to organize the information. The first column shows the possible sports first trimester. The first row show the possible sports second trimester. Inside the chart are the possible sports third trimester. This shows the different possible groups of sports a student may play. a. opy and complete the table below. 2nd Trimester B V 1st Trimester S T G b. How many different groups of three sports are possible for a student to be assigned in one year based on your table? How did you find the answer? Step 4: ssume students are randomly scheduled into a sport each trimester. What is the probability a student will be enrolled in tennis, basketball and dodgeball? (tennis, basketball, dodgeball) = number of times tennis, basketball, dodgeball listed = total number of different groups of sports listed Step 5: In this Explore! you listed the possible outcomes three different ways using a list, a tree diagram and a chart. Which one did you like best for organizing the information and counting the possible outcomes? Explain. Listing the possible outcomes shows a sample space. In the Explore! you listed the possible outcomes for sports that could be played by a person in E for one year. It is important to be able to see and count the number of possible outcomes in a sample space to find probabilities. Lesson 2-G ~ ompound robabilities Using Lists, Tree iagrams nd Tables 29

3 EXMLE 1 Solution You are packing for a trip. You decide to take four shirts (red, blue, green and yellow) and three shorts (, and ). How many outfits are possible? hoose one of the methods below to organize the information and see all the possible outfits. red blue Tree iagram List Table Shirt Shorts Shirt, Shorts green yellow red, red, red, blue, blue, blue, green, green, green, yellow, yellow, yellow, laid laid laid laid laid There are 12 different outfits possible. olling a number cube and tossing a coin are two separate events. You can make a list to show the 12 possible outcomes. 1, Heads 3, Heads 5, Heads 1, Tails 3, Tails 5, Tails 2, Heads 4, Heads 6, Heads 2, Tails 4, Tails 6, Tails What if you wanted to find the probability of rolling an odd number and the coin landing tails? This would be an example of finding a compound probability. compound probability is the probability of two or more events occurring. Sometimes the events are independent, which means one does not affect the other. olling a number cube and tossing a coin are independent events. Sometimes the events are dependent events, which means one event depends on the other event. hoosing one card from a deck of cards, keeping it, and then choosing a second card is an example of dependent events. By keeping the first card you have changed the possible cards to choose from the second time. To find a compound probability make a list, tree diagram or table to count the number of possible outcomes (sample space) and count the number of favorable outcomes (events). There were 12 possible outcomes for rolling a number cube and tossing a coin. Three of them showed rolling an odd number and tossing tails (1, Tails; 3, Tails; 5, Tails). (rolling odd number, Tails) = 3 = Lesson 2-G ~ ompound robabilities Using Lists, Tree iagrams nd Tables

4 EXMLE 2 indy has three letter cards that spell out the word. indy picks three cards, one at a time, without replacing them. What is the probability that she spells the word in the correct order? Solution reate a tree diagram showing the possible combinations. ount the number of possible outcomes. ount the number of favorable outcomes. 6 total outcomes,, 1 favorable outcome Find the probability. (,, ) = 1 6 EXMLE 3 Solution LaSean spins the spinner at the right two times. Find the probability that he spins a 3 and then a number greater than 1. Organize the information by making 1, 1 2, 1 3, 1 4, 1 a list. The spins are listed in order: 1, 2 2, 2 3, 2 4, 2 first spin, second spin. 1, 3 2, 3 3, 3 4, 3 1, 4 2, 4 3, 4 4, ount the number of possible outcomes in the sample space. There are 16 possible outcomes in the list. ount the number of favorable outcomes 3, 2 3, 3 3, 4 in the sample space. There are three favorable outcomes. Find the probability. (3, number > 1) = 3 16 Lesson 2-G ~ ompound robabilities Using Lists, Tree iagrams nd Tables 31

5 EXEISES Use a list to organize the possible outcomes for each experiment. Write the number of possible outcomes listed. 1. oll a number cube and toss a coin. 2. Spin two different spinners Spinner 1 B Spinner 2 3. Toss two coins. 4. Toss three coins. Use a tree diagram to organize the possible outcomes for each experiment. Write the number of possible outcomes shown. 5. hoose between three hats (baseball, visor or knit) and two pairs of shoes (cleats, boots). 6. hoose one cone (sugar or waffle), one scoop of ice cream (vanilla, chocolate or strawberry) and one topping (cherry or syrup). 7. ick one card (1, 2 or 3), toss a coin and roll a number cube. Use a table to organize the possible outcomes for each experiment. Write the number of possible outcomes shown. 8. oll two number cubes 9. Spin two different spinners B Spinner 1 Spinner 2 Find the number of possible outcomes for each situation using a list, tree diagram or table. Show your work. 10. You are buying T-shirts for your sports team. The shirts come in three colors (blue, red, or white) and can be either short sleeved or long sleeved. How many T-shirts are possible? 11. Jar contains two marbles (green and white). Jar B contains three marbles (blue, yellow and red). Jar contains two marbles (purple and pink). How many outcomes are possible if you choose one marble from each jar? 32 Lesson 2-G ~ ompound robabilities Using Lists, Tree iagrams nd Tables

6 12. t a restaurant you can choose one entrée (beef or chicken), one side dish (potatoes, green beans, rice or french fries) and one dessert (cake or ice cream). How many dinners are possible? 13. edro is leaving on a trip. He packs three shirts (blue, green and ), two pairs of shorts ( and navy) and three pairs of shoes (tennis, sandals and flip-flops). How many different outfits are possible? 14. You toss two coins and roll a number cube. How many outcomes are possible? Find each probability. Use a list, tree diagram or table to identify the favorable outcomes and the sample space. 15. Find the probability of rolling two 1s in a row using a number cube. 16. Toss three coins. Find the probability of tossing exactly two heads. 17. Toss three coins. Find the probability of tossing at least two heads. 18. Tabitha has a deck of cards numbered She picks one card, puts it back in the deck and then chooses a second card. What is the probability that she picks an even number and then a 3? 19. Javier has a deck of cards numbered 1-10 and a number cube. He chooses one card and rolls the number cube. What is the probability that he picks a number divisible by 5 and rolls a 5? 20. Tim has cards with the letters E, B, K, I on them. He picks one card, keeps it and then picks the next card until all cards are chosen. What is the probability Tim picks cards in the order B, I, K, E? 21. Kim has three jars holding marbles. The first jar has a red, green and yellow marble. The second jar has a blue and white marble. The third jar has a pink, and marble. Kim picks a marble from each jar without looking. What is the probability she has a red, a white and a pink marble in her hand? 22. ylan has a bag with 4 green marbles and 2 blue marbles. She takes one marble out of the bag and sets it on the table. Then, without replacing the marble, she chooses a second marble. What is the probability she chooses a green and a blue marble in any order? 23. Trent is making a sandwich. He has two breads to choose from (white or wheat), three meats to choose from (turkey, roast beef or ham), two vegetables to choose from (tomato or lettuce) and two condiments to choose from (mustard or mayonnaise). Trent randomly picks one bread, one meat, one vegetable and one condiment. What is the probability his sandwich is turkey and lettuce on wheat bread with mustard? Lesson 2-G ~ ompound robabilities Using Lists, Tree iagrams nd Tables 33