Math 3
Introduction to Expected Value
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1. Describe the relationship between the falling chip and coin flipping. 2. Write a polynomial, raised to a power, to model this game. 3. Find the probability that the chip falls into the center slot of $10,000 win. 4. Find the probability that the chip falls into a $0 slot. Note there are two such slots. 5. What is the probability of winning $1000? 500? 100? 6. How much, on average, would you win per chip if you were to keep playing this game for a long, long time? The average amount you would win, per chip, if you played the plinko game for a long time is called the expected value. We can calculate expected value this way only if the outcomes are numbers. To calculate expected value, we can assign a numerical value to each output: Plinko chip landing in the middle slot  Rolling a 3 on a number cube  Flipping a head on a coin  A random variable is a function whose inputs are outcomes, and whose outputs are numbers. Let X = the amount won in a game of plinko. 𝑥! = the possible values of the random variable 𝑝! = the probabilities of the values Winnings (𝑥! ) Probability (𝑝! ) 𝑥! ∙ 𝑝! $10,000 $1000 $500 $100 $0 𝐸 𝑋 = Example. Toss five coins. What is the expected value of the number of heads? Let H = Example. A local market has a prize wheel. Lucky customers can spin the wheel to win free fish. On one spin, it is possible to win 1 fish, 2 fish, 3 fish, or 10 fish. What is the expected value for the number of fish won on a single spin? What is the expected value for the total number of fish won on 3 spins? Homework: Read “Developing Habits of Mind” on p. 187 and on p.193 p. 195-­‐196 #3-­‐10