The document provides lesson material on probability and odds, including definitions, examples and practice problems. It defines key terms like probability, complementary events, odds, and discusses how to calculate probabilities and odds for various scenarios. Practice problems ask students to calculate probabilities and odds based on given information, such as the likelihood of random outcomes or events.

1. Lesson 12.7 , For use with pages 685-689 1. a dog 2. a cat or rabbit An animal shelter has 12 dogs, 15 cats, 2 snakes, and 3 rabbits. Find the probability of randomly selecting an animal.

2. Lesson 12.7 , For use with pages 685-689 1. a dog 2. a cat or rabbit An animal shelter has 12 dogs, 15 cats, 2 snakes, and 3 rabbits. Find the probability of randomly selecting an animal. ANSWER 3 8 ANSWER 9 16

3. Probability and Odds Section 12.7 P. 685

4. Essential Questions What are the differences between permutations and combinations? What are the differences between odds and probability? How is probability used to make predictions? What are the differences between experimental and theoretical probabilities?

5. Vocabulary Probability: Number of favorable outcomes Number of possible outcomes P (flip a head) = ½ P (flip a tail) = ½ P (flip heads or tails) = 1 P(rain) = 80% What is the probability it won’t rain? 20%

6. Vocabulary Complementary: Two events are COMPLEMENTARY when one event or the other (but NOT both) must occur. The sum of the probabilities of a complementary event is always 1. If events A & B are complementary, the P(event A) = 1 – P(event B)

7. EXAMPLE 1 Finding Probabilities Gifts a. What is the probability that your name is chosen? b. What is the probability that your name is not chosen? You and seven friends contribute money for a gift. Everyone’s name is put in a hat. The person whose name is chosen at random picks the gift.

8. EXAMPLE 1 SOLUTION a. P ( your name is chosen ) b. P ( your name is not chosen ) = 1 – P ( your name is chosen ) . Finding Probabilities = Number of favorable outcomes Number of possible outcomes = 1 8 = 1 – 1 8 = 7 8

9. GUIDED PRACTICE for Examples 1 and 2 You are given the probability that event A will occur. Find the probability that event A will not occur. ANSWER P (A) will not occur = 1 – P (A) 1. P ( A ) = 3 4 3 = 1 – 4 = 1 4

10. GUIDED PRACTICE for Examples 1 and 2 = 1– 0.45 = 0.55 You are given the probability that event A will occur. Find the probability that event A will not occur. 2. P (A) = 0 . 45 ANSWER P (A) will not occur = 1 – P (A)

11. GUIDED PRACTICE for Examples 1 and 2 You are given the probability that event A will occur. Find the probability that event A will not occur. 3. P (A) = 32% ANSWER P (A) will not occur = 1– 32% = 68% = 1 – P (A)

12. GUIDED PRACTICE for Examples 1 and 2 P ( drawings on S ) SOLUTION The 11 letters in the word MISSISSIPPI are each written on pieces of paper and randomly chosen from a bag. What is the probability of drawing an S from the bag? What is the probability of not drawing an S? 5. = 4 11 Number of favorable outcomes Number of possible outcomes =

13. GUIDED PRACTICE for Examples 1 and 2 P (Not drawings on S) = 1 – 4 11 = 7 11 1 – P (drawings on S) =

14. Vocabulary Odds: Number of favorable outcomes Number of unfavorable outcomes Odds: probability event will occur probability event will NOT occur

15. Odds of rolling a 3 on a dice: Favorable: 3 Unfavorable: 1, 2, 4, 5, 6 Odds = 1/5 Odds of not rolling a 3 on a dice: Favorable: 1, 2, 4, 5, 6 Unfavorable: 3 Odds: 5/1

16. EXAMPLE 2 Finding Odds Vacation Survey You do a survey asking your class to rank three vacation choices Results for “the beach” are shown at the right. What are the odds in favor of a randomly chosen student from your class ranking a beach vacation first?

17. EXAMPLE 2 The beach was ranked first by 6 students, so there are 6 favorable outcomes. It was ranked second by 12 students, and ranked third by 9 students, so there are 12 +9 = 21 unfavorable outcomes. Odds in favor SOLUTION Finding Odds ANSWER The odds in favor of a randomly chosen student ranking a beach vacation first are 2 to 7 . Number of unfavorable outcomes Number of favorable outcomes = = 6 21 = 2 7

18. GUIDED PRACTICE for Examples 1 and 2 Odds in favor You choose a card at random from a set of cards numbered 1 to 24 . Find the odds in favor of the event. SOLUTION 6. You choose a 10 . = Number of unfavorable outcomes Number of favorable outcomes = 1 23

19. GUIDED PRACTICE for Examples 1 and 2 7. You choose an odd number. Odds in favor No. of odd numbers from 1 to 24 are 12 SOLUTION You choose a card at random from a set of cards numbered 1 to 24 . Find the odds in favor of the event. = Number of unfavorable outcomes Number of favorable outcomes = 12 12 = 1/1

20. GUIDED PRACTICE for Examples 1 and 2 No. of even numbers greater than 8 between 1 to 24 are 8 Odds in favor 8. You choose an even number greater than 8 . SOLUTION You choose a card at random from a set of cards numbered 1 to 24 . Find the odds in favor of the event. = Number of unfavorable outcomes Number of favorable outcomes 1 2 = 8 16 =

21. EXAMPLE 3 Finding Odds Using Probability Basketball Sean makes 65% of his free throws. What are Sean’s odds in favor of making a free throw? SOLUTION Odds Write percents as decimals . Subtract. = 0 . 65 0 . 35 0 . 65 1 – 0 . 65 =

22. EXAMPLE 3 ANSWER Sean’s odds in favor of making a free throw are 13 to 7 . Finding Odds Using Probability or 13 7 Multiply by . Then simplify. 100 100 = 65 35 ,

23. GUIDED PRACTICE for Example 3 Odds Subtract. Write percents as decimals SOLUTION ANSWER Sean’s odds in favor of making a free throw are 17 to 3. = 0.85 0.15 85 15 = 17 or 3 Suppose Sean makes 85 % of his free throws. What are Sean’s odds in favor of making a free throw? 9. 0.85 1 – 0.85 = Multiply by . T hen simplify . 100 100

24. Assignment: P. 687 #1-6, 11-20 Remember: Answers must be in simplest form (always)!