Foreigner - Cold as Ice https://www.youtube.com/watch?v=g_1XdSqBQUg

Number of mph over speed limit 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? Number of mph over speed limit 10-15 >15 Total Wearing Seatbelt Yes 65 145 210 No 15 75 90 80 220 300

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

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)

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)

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

Interpreting Expected Value If you get a ZERO expected 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

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

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

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

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?

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