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Warm-up

Warm-up. Use the table to answer the questions. What is the probability that someone wearing their seatbelt was going >15 mph over speed limit? What is the probability that someone was going 10-15 mph OR was not wearing a seatbelt?. Expected Value.

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Warm-up

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  1. Warm-up Use the table to answer the questions. What is the probability that someone wearing their seatbelt was going >15 mph over speed limit? What is the probability that someone was going 10-15 mph OR was not wearing a seatbelt?

  2. Expected Value • Essential Question - What is expected value used for in real-life?

  3. What it is and what it is used for • A weighted average • The expected results of an experiment in the long run. • Used in business to predict future profits • Used in insurance to determine how much a person’s insurance rate • Used in games such as the lottery, slot machines, roulette to determine expected winnings (or losses)

  4. How you find it • Multiply each probability by amount you will win and then add all together • Used in business to predict future profits • Used in insurance to determine how much a person’s insurance rate • Used in games such as the lottery, slot machines, roulette to determine expected winnings (or losses)

  5. Example • I will give you $1 if you roll an even number on a die and you give me $1 if you roll an odd number. • Who would win money in the long run? • (prob of even)($1)+(prob of odd)(-$1) • If the expected value is 0, the game is called FAIR

  6. Interpreting Expected Value • If you get a ZEROexpected value, you expect to BREAK EVEN in the long run • If you get a POSITIVE expected value, you expect to WIN in the long run • If you get a NEGATIVE expected value, you expect to LOSE in the long run • The value you get for expected value will probably NOT be one of the winnings of the game

  7. Example 2 • If you roll a 1, I will give you $4 and if you don’t roll a 1, you give me $1. • What is the expected value? Does this mean you will win or lose money? • (prob of 1)($4) + (prob of NOT 1)(-$1) • You will lose money over time

  8. Example 3 • Suppose it costs $5 to spin the spinner and you win the amount you spin. • What is your expected value? Should you play? • p(2)($2-$5)+p(10)($10-$5)+p(1)($1-$5) • You should not play if you want to win money

  9. Example 4 You are taking a multiple choice test that has 4 possible answers for each question. You get 3 points for each correct answer and lose 1 point for each incorrect answer, and do not gain or lose any points for answers left blank. If you do not know the answer to a question should you guess an answer to a question you don’t know? Hint:1. Find the probability of each outcome. 2. Find the expected value of guessing the answer

  10. Can we make money? At a roulette wheel there are 2 zeroes and 36 non zero numbers (18 red and 18 black) to bet on. If I bet $1 on red what is the expected value of my bet? How about after 10 of the same bets? How much can I be expected to win or lose?

  11. $300 $600 $500 $100 $800 $700 $200 $400 Spinner What is the expected value of the spinner? B. A. D. C.

  12. Tables Use your formula and calculate (.25) 3 + (.30) 4 + (.10) 13 + (.35) 2 = .75 + 1.20 + 1.30 + .70 = 3.95

  13. Tables Find the expected value of the following event. 1 30 A. B. C. 173.8 D. 6.85

  14. Classwork • In a group with NO MORE than 4 people, you will calculate the expected value of a single one dollar scratch off lottery ticket. Show the calculations you did to get the answer, even if you used a calculator. • If you purchased 1000 of these tickets, what would your net loss be? • Would it help your expected winnings if you and 9 other people bought a total of 100 tickets in the your lottery ticket game and split your earnings?  Why or why not?  (In other words, would you win more by pooling your resources with 9 others rather than buying only 10 tickets yourself?) • How does computing expected value of these tickets help a person to maintain a sensible perspective on purchasing lottery scratch game tickets?

  15. Homework pg. 357 #1-9 **Remember to check the ODDS in the back of the book!***

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