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Warm-up #1

Warm-up #1. 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 #1

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  1. Warm-up #1 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 • 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 • Probabilities are P • The values of the events are x • Expected outcome is E • E = p1x1 + p2x2 +p3x3 …..pnxn • Multiply each probability by the amount you will win or lose then add them all together.

  5. 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

  6. Example 1 • 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

  7. Example 2 You are taking a 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 is it to your advantage to 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

  8. Answer • Each question has 4 possible answers; only 1 is correct. Guessing correctly is ¼ and guessing incorrectly is ¾ 2. Multiply the points gained or lost by the correspoding probability. 3 for correct, -1 for incorrect so…. E = 3(1/4) + (-1) (3/4) = 0 ¾ - ¾ = 0 so what is your answer? Is it advantageous to guess if you don’t know the answer???

  9. 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?

  10. Did I win? My chance of winning $1 is 18/38 and my chance of losing $1 (or winning -$1) is 20/38. My expected value, E = (18/38) ( 1 ) + (20/38 )( -1) = 18/38 - 20/38 = -2/38 = -5.26%. I can expect to lose .0526 every spin of the wheel After 10 bets I will lose 52.6 = 53 cents.

  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

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