Expected Value Lesson Essential Question: How do we use expected value to predict outcomes? Standards: MM1D2. Students will use the basic laws of probability. d. Use expected value to predict outcomes.

Let’s review expected value… Example 1: Trey is organizing a carnival game. In this game the player has to spin the spinner pictured to the right. The player can win the amount shown on the spinner. If the player has to pay $2.00 to play the game, what can the player expect to earn on each spin? $0 $1.00 $2.00 $10.00 Write down the important stuff before moving to the next slide

Begin by listing the possible outcomes $0 $1 $2 $10

Next find the probability of each possible outcome. $0 3/6 or 1/2 $1 1/6 $2 1/6 $10 1/6

Now you multiply the possible outcomes by the probability they occur and add the values you multiplied. Possible Outcome Probability $0 3/6 or 1/2 x $1 1/6 1/6 $2 $10 1/6 = = 2.17

Here is another way to look at it… $0 $1.00 $2.00 $10.00 If the chances are equal, then you can simply add the values then divide by how many you added (find the average) 0 + 1 + 0 + 2 + 0 + 10 = 13 13/6 = 2.17

That means that the player can expect to earn $0.17 on each spin. Almost done. Remember that the player has to pay $2.00 to play. In order find how much the player will earn, we have to subtract the $2.00 from the expected value. $2.17 - $2.00 = $0.17 That means that the player can expect to earn $0.17 on each spin.

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Example 2: Chase is playing a game with a dice. If he rolls a 2, 4, or 6, he wins $5.00. If he rolls a 3 or 5 he wins $8.00. If he rolls a 1, he wins $20.00. On average how much can Chase expect to earn from one roll? $33.00 $8.50 $5.50

Incorrect Take another look, make sure you are identifying each possibility.

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