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

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 Course Theoretical Probability

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? 1 16 __ Course Theoretical Probability

Learn to find the theoretical probability and complement of an event. Course Theoretical Probability

Vocabulary theoretical probability equally likely fair complement Insert Lesson Title Here Course Theoretical Probability

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. Course Theoretical Probability

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. Course Theoretical Probability

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. P(3)= 3 possible outcomes _________________ There is only one way for the spinner to land on 3. P(3)= 3 possible outcomes __________________ 1 way event can occur = 1 3 __ Course Theoretical Probability

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. P(greater than 4)= 6 possible outcomes _________________ P(greater than 4)= 6 possible outcomes ____________________ 2 ways events can occur = 1 3 __ Course Theoretical Probability

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. P(3)= 3 possible outcomes _________________ There are two ways for the spinner to land on 1 or 2. P(3)= 3 possible outcomes __________________ 2 ways event can occur = 2 3 __ Course Theoretical Probability

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. P(less than 4)= 6 possible outcomes _________________ P(less than 4)= 6 possible outcomes ____________________ 3 ways events can occur = 1 2 __ Course Theoretical Probability

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

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% _____ _____ Subtract 45% from each side. Course Theoretical Probability

Course Theoretical Probability 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% -35% -35% _____ _____ Subtract 35% from each side.

Lesson Quiz Use the spinner shown for problems 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? Insert Lesson Title Here 98% 2 7 __ Course Theoretical Probability