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Splash Screen. Five-Minute Check (over Lesson 12–6) Then/Now New Vocabulary Example 1: Real-World Example: Experimental Probability Example 2: Real-World Example: Simulation Example 3: Real-World Example: Theoretical and Experimental Probability. Lesson Menu. A B C D.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 12–6) Then/Now New Vocabulary Example 1: Real-World Example: Experimental Probability Example 2: Real-World Example: Simulation Example 3: Real-World Example: Theoretical and Experimental Probability Lesson Menu

  3. A B C D If you spin the spinner two times, how many outcomes are possible? A. 10 B. 9 C. 8 D. 7 5-Minute Check 1

  4. A B C D A. B. C. D. The spinner is spun two times. What is the probability distribution of X, where X represents the number of times the spinner lands on green for X = 0, X = 1, and X = 2? 5-Minute Check 2

  5. A B C D A. B. C.D. The spinner is spun two times. Make a probability histogram for X,where X represents the number of times the spinner lands on green for X = 0, X = 1, and X = 2. 5-Minute Check 3

  6. A B C D A. B. C. D. On a random roll of two dice, what is the probability that the sum of the two numbers showing is greater than 10? 5-Minute Check 4

  7. You used probability distributions. (Lesson 12–6) • Design simulations to estimate probabilities. • Summarize data from simulations. Then/Now

  8. theoretical probability • experimental probability • relative frequency • empirical study • simulation • expected value Vocabulary

  9. Experimental Probability A. MEDICAL RESEARCH Researchers at a pharmaceutical company expect a new drug to work successfully in 70% of patients. To test the drug’s effectiveness, the company performs three clinical studies of 100 volunteers who use the drug for six months. The results of the studies are shown in the table. What is the experimental probability that the drug was successful for Study I? Example 1

  10. Answer: The experimental probability of the drug being successful in Study 1 is or 61%. Experimental Probability Example 1

  11. Experimental Probability B. MEDICAL RESEARCH Researchers at a pharmaceutical company expect a new drug to work successfully in 70% of patients. To test the drug’s effectiveness, the company performs three clinical studies of 100 volunteers who use the drug for six months. The results of the studies are shown in the table. What is the experimental probability that the drug would cause a patient to show no improvement for all three studies? Example 1

  12. Answer: The experimental probability of the drug causing no improvement in all three studies is or about 32%. Experimental Probability Example 1

  13. A B C D A. Hernando plays on his high school football team as the kicker. He has been practicing field goals. He says he hopes to make at least 75% of the field goals he takes. To test this, he records the number of field goals he takes during the regular season and playoff games. The information is in the table below.What is the probability that Hernando successfully makes his field goals during the regular season? A. about 67% B. about 71% C. about 75% D. about 79% Example 1

  14. A B C D B. Hernando plays on his high school football team as the kicker. He has been practicing field goals. He says he hopes to make at least 75% of the field goals he takes. To test this, he records the number of field goals he takes during the regular season and playoff games. The information is in the table below.What is the experimental probability that Hernandez misses his field goals during the regular season and playoff combined? A. about 19% B. about 21% C. about 23% D. about 27% Example 1

  15. Simulation A. Miguel makes 50% of the basketball free throws he attempts. What could be used to simulate Miguel’s free-throw attempts? Explain. Answer: A coin can be used. Since the probability of Miguel making a free throw is 50% and the probability of the coin being flipped and landing on heads is 50%, the coin can simulate the free throw. Heads can represent a made free throw and tails can represent a missed free throw. Example 2

  16. Simulation B. Miguel makes 50% of the basketball free throws he attempts. Describe a way to simulate the next 20 free-throw attempts. Answer: Toss the coin to simulate one attempt. Record the result and repeat 19 more times. Example 2

  17. A B C D A. Amarita runs a newspaper route. While riding her bicycle, she has a 75% chance of throwing the newspaper and landing it on the driveway.Which of the following could be used to simulate Amarita throwing the newspaper? A. A spinner could be created with four equally sized spaces, three of which are colored red. If the spinner lands on a red space, then Amarita missed the driveway with the newspaper. B. A spinner could be created with four equally sized spaces, three of which are colored blue. If the spinner lands on a blue space, then Amarita threw the newspaper onto the driveway. C. A die is rolled. If the die comes up 1 or 2, then Amarita threw the newspaper onto the driveway. D. A die is rolled. If the die comes up as an odd number, then Amarita threw the newspaper onto the driveway. Example 2

  18. A B C D B. Amarita runs a newspaper route. While riding her bicycle, she has a 75% chance of throwing the newspaper and landing it on the driveway.Describe a way to simulate the paper throw if the paper landed on the driveway 2 out of 3 times. A. A spinner could be created with three equally sized spaces, two of which are colored red. If the spinner lands on a red space, then Amarita missed the driveway with the newspaper. B. A die is rolled. If the die comes up an even number, then Amarita threw the newspaper onto the driveway. C. A spinner could be created with three equally sized spaces, one of which is colored blue. If the spinner lands on a blue space, then Amarita hit the driveway with the newspaper. D. A die is rolled. If the die comes up as less than or equal to four, then Amarita threw the newspaper onto the driveway. Example 2

  19. Theoretical and Experimental Probability A. DOGS Ekta raises purebred dogs. One of her dogs had a litter of four puppies. What objects can be used to simulate the possible outcomes of the genders of the puppies? Answer: Use a simulation where 1 out of 2 objects represents a male, and the other object represents a female. One possible simulation would be to toss four coins, one for each puppy, with heads representing female and tails representing male. Example 3

  20. = Answer: The theoretical probability is or 37.5%. Theoretical and Experimental Probability B. DOGS Ekta raises purebred dogs. One of her dogs had a litter of four puppies. Find the theoretical probability that there are two females and two male puppies. If you list out all possibilities of the puppies’ gender, there are 16 different possible outcomes. Out of these possibilities, 6 of them include 2 female puppies and 2 male puppies. Example 3

  21. Theoretical and Experimental Probability C. DOGS Ekta raises purebred dogs. One of her dogs had a litter of four puppies. The results of a simulation Ekta performed are shown in the table. What is the experimental probability that there are exactly three male puppies? Example 3

  22. Theoretical and Experimental Probability D. DOGS Ekta raises purebred dogs. One of her dogs had a litter of four puppies. How does the experimental probability compare to the theoretical probability of a litter with three males? Answer: The experimental probability, 24%, is very close to the theoretical probability, 25%. Example 3

  23. A B C D A. ICE CREAM At a local diner, only two flavors of ice cream are served. Since the manager prefers mint ice cream over strawberry ice cream, there is a chance that the flavor of the day will be mint. What objects can be used to simulate the possible outcomes of the flavor of the day? A. A spinner could be created with four equally sized spaces, three of which are colored red. If the spinner lands on a red space, then the flavor of the day will be strawberry. B. A coin is tossed, if it lands on heads, then the flavor of the day will be mint. C. A die is rolled, if it lands on a 3 or a 5, then the flavor of the day is mint. D. A spinner could be created with four equally sized spaces spaces, three of which are colored blue. If the spinner lands on a blue space, then the flavor of the day will be mint. Example 3

  24. A B C D B. ICE CREAM At a local diner, only two flavors of ice cream are served. Since the manager prefers mint ice cream over strawberry ice cream, there is a chance that the flavor of the day will be mint. Find the theoretical probability that the flavor of the day will be strawberry. A. 20% B. 25% C. 33% D. 50% Example 3

  25. A B C D C. ICE CREAM At a local diner, only two flavors of ice cream are served. Since the manager prefers mint ice cream over strawberry ice cream, there is a chance that the flavor of the day will be mint. The results of the most recent days of the diner’s menu are shown in the table. What is the experimental probability that the flavor of the day will be mint? A. 70% B. 75% C. 78% D. 80% Example 3

  26. A B C D D. ICE CREAM At a local diner, only two flavors of ice cream are served. Since the manager prefers mint ice cream over strawberry ice cream, there is a chance that the flavor of the day will be mint. The results of the most recent days of the diner’s menu are shown in the table. How does the experimental probability compare to the theoretical probability of the flavor of the day being mint? A. The experimental probability is close to the theoretical probability. B. The experimental probability is equal to the theoretical probability. C. The experimental probability is very different from the theoretical probability. D. The experimental probability is not comparable to the theoretical probability. Example 3

  27. End of the Lesson

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