1. 11-3 Theoretical Probability Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Warm Up Tim took one marble from a bag, recorded the color, and returned it to the bag. He repeated this several times and recorded the results. 1. Find the experimental probability that a marble selected from the bag will be green. 2. Find the experimental probability that a marble selected from the bag will not be yellow. Course 1 11-3 Theoretical Probability 3 5 __ 4 5

3. Problem of the Day What is the probability that the sum of four consecutive whole numbers is divisible by 4?. 0 Course 1 11-3 Theoretical Probability

4. Learn to find the theoretical probability of an event. Course 1 11-3 Theoretical Probability

5. Vocabulary theoretical probability equally likely fair Insert Lesson Title Here Course 1 11-3 Theoretical Probability

6. 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 1 11-3 Theoretical Probability

7. 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 1 11-3 Theoretical Probability

8. Additional Example 1A: Finding Theoretical Probability A. What is the probability that this fair spinner will land 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 1 11-3 Theoretical Probability

9. Additional Example 1B: Finding Theoretical Probability B. 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 = 2 6 __ Course 1 11-3 Theoretical Probability

10. Try This: Example 1A A. What is the probability that this fair spinner will land on 1? 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 1. P(3)= 3 possible outcomes __________________ 1 way event can occur = 1 3 __ Course 1 11-3 Theoretical Probability

11. Try This: Example 1B B. 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 1 11-3 Theoretical Probability

12. Think about a single experiment, such as tossing a coin. There are two possible outcomes, heads or tails. What is P(heads) + P(tails)? Experimental Probability (coin tossed 10 times) Theoretical Probability H T llll l llll P(heads) = P(tails) = + 6 10 __ 4 10 __ 10 __ == 1 6 10 __ 4 10 __ P(heads) = P(tails)= 1 2 __ 1 2 + 1 2 2 2 == 1 Course 1 11-3 Theoretical Probability __ 2 1

13. No matter how you determine the probabilities, their sum is 1. This is true for any experiment—the probabilities of the individual outcomes add to 1 (or 100%, if the probabilities are given as percents.) Course 1 11-3 Theoretical Probability

14. Additional Example 2: Finding Probabilities of Events not Happening 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 1 11-3 Theoretical Probability

15. Course 1 11-3 Theoretical Probability Try This: 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.

16. 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? Insert Lesson Title Here 98% 2 7 __ 4 7 4 7 Course 1 11-3 Theoretical Probability