Probability & odds

1. Probability & odds

2. Will the Lakers or Spurs be more likely to win the game? What are the possibilities of rain today? What is the chance of drawing an ace from a deck of cards?

3. Probability • The probability of an event is a ratio that tells how likely it is that an event will take place. The numerator is the number of favorable outcomes and the denominator is the number of possible outcomes.

4. Example 1 When you toss a die, there are six ways it can fall. The probability of getting a “2” on one roll is 1/6.

5. Definition of Probability

6. Example 2 • “Suppose you have 7 notebooks, 3 of which are blue, 1 red, 2 green, and 1 yellow. If you select one at random, do you have a greater chance of choosing any one color? • What 2 colors do you have an equal chance of selecting?” • Answer: Yes, blue: red & yellow

7. Real life probability • Sports event • Passing a score on a test • Predicting the homecoming queen

8. Example 3 Thomas has a collection of CDs that he plays regularly. He has 6 rock CDs, 3 country CDs, & 4 movie sound track CDs. If Thomas chooses a CD @ random, what is the probability that he will get a country CD?

9. Example 4 Kendra has a collection of various cereals on a shelf in the cabinet. 5 of the cereals contain corn, 2 contain rice, & 4 contain oats. Without looking, she selects a box of cereal for breakfast. What is the probability that the cereal she selects will contain oats?

10. Example 5 Lynn collects stamps from different countries. She has 5 from Canada, 2 from France, 1 from Russia, 4 from Great Britain, and 1 from Germany. If she accidentally loses 1 stamp, what is the probability that it is the stamp from Russia?

11. Example 6 • Grace has a collection of jerseys from college campuses that she has visited. 2 jerseys come from colleges in IN, 3 from CA, 1 from OH, 1 from NV, & 3 from NY. If she grabs a jersey without looking, what is the probability that she will grab one from IN?

12. Where Probability will land… • The probability of any event is always a value from 0 to 1. • If the probability of an event is 0, it is impossible for that event to occur. • An event that is certain to occur has a probability of 1.

13. Example 7 Suppose a weather forecaster states that the probability of rain today is .25 or ¼. This means that the probability that it will not rain is 0.75 or ¾. The odds that it will rain today are 1:3. the odds that it will not rain today are 3:1.

14. How do they get that answer ? • An event that is certain to happen has a probability of 1. • It is certain that it will either rain or not rain. • Therefore, if the probability of rain is 0.25, the probability of no rain is (1-0.25) or 0.75. • If the probability of rain is 0.25, that is 25/100 or 1 chance out of 4 that it will rain. • Therefore, the possible successes to the possible failures would be 1 to 3.

15. Definition of Odds.: The odds of an event occurring is the ratio of the number of ways the event can occur (successes) to the number of ways the event cannot occur (failures.) Odds = successes : failures

16. Example 8 11 poker chips are #ed consecutively 1 – 10, with 2 of them labeled with a 6 & placed in a jar. A chip is drawn @ random, find the probability of drawing a 6.

17. Example 9 • Find the odds of drawing a 6 from the jar above. • Find the odds of not drawing a 6. • Odds of drawing 6 = # of chances to draw 6 : # of chances to draw other #’s • Odds of drawing 6 = 2:9 (Read as “2 to 9”) • Odds of not drawing a 6 = # of chances to draw other #s: # of chances to draw 6 • Odds of not drawing a 6 = 9: 2

18. Example 10 The door prize at a party with 25 people is given by writing numbers 1 – 25 on the bottom of the paper plates used. What is the probability that an individual had the winning plate?

19. Example 11 • What are the odds of winning the door prize above? • What are the odds of not winning the door prize? • Odds of winning = 1:24 • Odds of not winning = 24:1

20. Now it’s your turn to work on these problems….