1. Section 4.6 Mathematical Expectation and Odds Warm up Warm up

2. Mathematical Expectation It is the expected monetary value of an event. It is the expected monetary value of an event. ME = $ ∙ p($)

3. 1) Mulvihill is bidding on a landscaping job so he can make some money for senior week. The profit for the Alapocas job should be about $3200 for the year with a probability of 0.87. The profit of the Hockessin job will be $3000 with a probability of 0.91. The profit for the Alapocas job should be about $3200 for the year with a probability of 0.87. The profit of the Hockessin job will be $3000 with a probability of 0.91. However, with the costs of running the landscaping he will lose $700 on equipment repairs with a probability of 0.39. However, with the costs of running the landscaping he will lose $700 on equipment repairs with a probability of 0.39. What is his expected return for each job? What is his expected return for each job?

4. 2) J anavel made up a new game using one die. If someone rolls an even number, they win $2. If they roll a one, they win $5. If they roll a 3 or a 5, they pay $4. It costs $2 to play. What is the mathematical expectation?

5. ODDS Odds in favor Odds in favor Formula: p to q Formula: p to q  p = want, q = don’t want Odds against Odds against Formula: q to p  p = want, q = don’t want

6. SHUT UP! The probability of Mrs. Godfrey telling the students to “Shut it” is 87%. The probability of Mrs. Godfrey telling the students to “Shut it” is 87%. –What are the odds in favor of her screaming “Shut it”? –What are the odds against her screaming “Shut it”?

7. World Series The Yankees have a ⅛ chance of winning the the World Series. The Yankees have a ⅛ chance of winning the the World Series. –What are the odds in favor of them winning? –What are the odds against them losing?

8. Deal or No Deal or No Deal In the Game Show Deal or No Deal, a contestant begins by choosing 1 of 26 numbered cases. Each case holds a different amount. Neither the host or the banker, who offers to buy the contestant’s case after each round, know what any case contains. In the Game Show Deal or No Deal, a contestant begins by choosing 1 of 26 numbered cases. Each case holds a different amount. Neither the host or the banker, who offers to buy the contestant’s case after each round, know what any case contains.

9. What is the probability that you choose the $1,000,000 case to begin with? What is the probability that you choose the $1,000,000 case to begin with? If you played the game many, many times, what is the expected value of the amount that your case contains? If you played the game many, many times, what is the expected value of the amount that your case contains? Worksheet Worksheet Worksheet

10. Play as a Class Record the following information in the table. Record the following information in the table.