Warm-up $100 $100 90° 90° 60° 60° $200 60° $400 $300 If you spin once, what is the probability of getting each dollar amount (fractions)? 2) If you spin twice, what is the probability of getting $100 and then $200? 3) If you spin twice, what is the probability of getting a sum of $600? 1/2, 1/6, 1/6, 1/6 1/12 1/12

When do you find the expected value of an experiment? Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: When do you find the expected value of an experiment? Standard: MM1D2.d.

Expected Value A collection of outcomes is partitioned into n events, no two of which have any outcomes in common. The probabilities of the n events occurring are p1, p2, p3,..., pn where p1 + p2 + p3 + pn = 1. The values of the n events are x1, x2, x3,..., xn. E = p1x1 + p2x2 + p3x3 + ... + pnxn

Example 1 Find the expected value. .20 2 .30 3 .10 4 .40 E = 1(.20) + 2(.30) + 3(.10) + 4(.40) = 2.7 If I do this experiment 10 times, what total value would you expect to get?

Example2 Find the expected value. Gain, x 10 15 20 30 Probability 0.20 0.30 E = 10(.20) + 15(.30) + 20(.30) + 30(.20) = 18.5 If I do this experiment 10 times, what total value would you expect to get?

Example 3 You take an exam that has 5 possible answers for each question. You gain 3 points for each correct answer, lose 1 point for each incorrect answer, and do not gain or lose points for blank answers. If you do not know the answer to a question is it to your advantage to guess the answer? E = (3)(1/5) + (-1)(4/5) = -1/5

E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500) Example 4 At a raffle, 2500 tickets are sold at $5 each for 3 prizes of $1000, $500, and $100. You buy one ticket. What is the expected value of your gain? Gain,x $995 $495 $95 -$5 Prob, p 1/2500 2497/ 2500 E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500) = -$4.36

Example 5 You have a box with two nickels, one dime, three quarters, and two half dollars. Find the expected value of removing one coin. Make a table of values and probabilities: Calculate the expected value: 5(0.25) + 10(0.125) + 25(0.375) + 50(0.25) = 24.375 cents Value 5 10 25 50 Probability 1/4 1/8 3/8

Homework Page 357 # 1 – 9 all We will spend the rest of class doing the spinner task. Quiz tomorrow (Wednesday) Review Thursday Test Friday

Test Review Ch 3 Counting and Probability Practice 16 – 19, 24, Chapter 3 Test Review 12 – 29 all