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12-4

Theoretical Probability. 12-4. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Theoretical Probability. 12-4. Course 1. Warm Up

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12-4

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  1. Theoretical Probability 12-4 Course 1 Warm Up Problem of the Day Lesson Presentation

  2. Theoretical Probability 12-4 Course 1 Warm Up A café offers a soup-and-sandwich combination lunch. You can choose tomato soup, chicken noodle soup, or clam chowder. You can choose a turkey, ham, veggie, or tuna sandwich. How many lunch combinations are there? 12

  3. Theoretical Probability 12-4 1 __ 16 Course 1 Problem of the Day Rory dropped a quarter, a nickel, a dime, and a penny. What is the probability that all four landed tails up?

  4. Theoretical Probability 12-4 Course 1 Learn to find the theoretical probability and complement of an event.

  5. Theoretical Probability 12-4 Course 1 Insert Lesson Title Here Vocabulary theoretical probability equally likely fair complement

  6. Theoretical Probability 12-4 Course 1 Another way to estimate probability of an event is to use theoretical probability. One situation in which you can use theoretical probability is when all outcomes have the same chance of occurring. In other words, the outcomes are equally likely.

  7. Theoretical Probability 12-6 Course 1 An experiment with equally likely outcomes is said to be fair. You can usually assume that experiments involving items such as coins and number cubes are fair.

  8. Theoretical Probability 12-4 P(3)= 1 __ = 3 1 way event can occur P(3)= __________________ _________________ 3 possible outcomes 3 possible outcomes Course 1 Additional Example 1A: Finding Theoretical Probability What is the probability of this fair spinner landing on 3? There are three possible outcomes when spinning this spinner: 1, 2, or 3. All are equally likely because the spinner is fair. There is only one way for the spinner to land on 3.

  9. Theoretical Probability 12-4 2 ways events can occur P(greater than 4)= 1 __ = 3 P(greater than 4)= _________________ ____________________ 6 possible outcomes 6 possible outcomes Course 1 Additional Example 1B: Finding Theoretical Probability What is the probability of rolling a number greater than 4 on a fair number cube? There are six possible outcomes when a fair number cube is rolled: 1, 2, 3, 4, 5, or 6. All are equally likely. There are 2 ways to roll a number greater than 4:5 or 6.

  10. Theoretical Probability 12-4 P(3)= 2 __ = 3 2 ways event can occur P(3)= __________________ _________________ 3 possible outcomes 3 possible outcomes Course 1 Check It Out: Example 1A What is the probability of this fair spinner landing on 1 or 2? There are three possible outcomes when spinning this spinner: 1, 2, or 3. All are equally likely because the spinner is fair. There are two ways for the spinner to land on 1 or 2.

  11. Theoretical Probability 12-4 3 ways events can occur P(less than 4)= 1 __ = 2 P(less than 4)= _________________ ____________________ 6 possible outcomes 6 possible outcomes Course 1 Check It Out: Example 1B What is the probability of rolling a number less than 4 on a fair number cube? There are six possible outcomes when a fair number cube is rolled: 1, 2, 3, 4, 5, or 6. All are equally likely. There are 3 ways to roll a number greater than 4:3, 2 or 1.

  12. Theoretical Probability 12-4 Course 1 When you combine all the ways that an event can NOT happen, you have the complement of the event.

  13. Theoretical Probability 12-4 Subtract 45% from each side. Course 1 Additional Example 2: Finding the Complement of an Event Suppose there is a 45% chance of snow tomorrow. What is the probability that it will not snow? In this situation there are two possible outcomes, either it will snow or it will not snow. P(snow) + P(not snow) = 100% 45% + P(not snow) = 100% -45% -45% _____ _____ P(not snow) = 55%

  14. Theoretical Probability 12-4 -35% -35% _____ _____ Subtract 35% from each side. Course 1 Check It Out: Example 2 Suppose there is a 35% chance of rain tomorrow. What is the probability that it will not rain? In this situation there are two possible outcomes, either it will rain or it will not rain. P(rain) + P(not rain) = 100% 35% + P(not rain) = 100% P(not rain) = 65%

  15. Theoretical Probability 12-4 2 4 4 __ __ __ 7 7 7 Course 1 Insert Lesson Title Here Lesson Quiz Use the spinner shown for problems 1-3. 1.P(2) 2.P(odd number) 3.P(factor of 6) 4. Suppose there is a 2% chance of spinning the winning number at a carnival game. What is the probability of not winning? 98%

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