Foreigner Cold as Ice https www youtube comwatch
• Foreigner - Cold as Ice https: //www. youtube. com/watch? v=g_1 Xd. Sq. BQUg
Warm-up Use the table to answer the questions. Number of mph over speed limit Wearing Seatbelt 1. 2. 10 -15 >15 Total Yes 65 145 210 No 15 75 90 Total 80 220 300 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 • 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 What is the expected value of the spinner? $300 $600 $500 $100 $800 $700 $200 $400
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