Expected Value MM1D2 Students will use the basic laws of probabilities. d. Use expected value to predict outcomes.

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Expected Value MM1D2 Students will use the basic laws of probabilities. d. Use expected value to predict outcomes.

Expected Value Expected value E of the collection of outcomes is the sum of the products of the events’ probabilities and their values.

Expected Value The expected value or mean of a discrete distribution is the long-run average of occurrences. We must realize that any one trial using a discrete random variable yields only one outcome. However, if the process is repeated long enough, the average of the outcomes are most likely to approach a long-run average, expected value or mean value.

Spinner Game

Spinner Game

Spinner Game

Spinner Game

Spinner Game

Spinner Game

Try some… Consider a game in which two players each choose an integer from 1 to 3. If the sum of the two integers is even, then player A scores 4 points and player B loses 2 points. If the sum is odd, then player B scores 4 points and player A loses 2 points. Find the expected value for player A.

Answer The possible outcomes are 1+1 2+1 3+1 1+2 2+2 3+2 1+3 2+3 3+3 1+1 2+1 3+1 1+2 2+2 3+2 1+3 2+3 3+3 The probability of an even sum is 5/9. The probability of an odd sum is 4/9. Player A: E = 4(5/9) + (-2)(4/9) = 12/9 =4/3

Project Create a spinner for a game. Make sure you have at least seven sections distributed into semicircles and cut angles. Each spinner section needs to have numbers, dollar amounts, etc. Determine the expected value of 10 spins, 20 spins, and 50 spins.

Rubric Spinner Rubric Group members: 3 2 1 Construction The spinner was neatly constructed with evenly distributed parts. The spinner was neat but did not have evenly distributed numbers. The spinner was constructed but was not neat. Reasoning The problem was set up correctly with explanations given. Formulas were used. The problem was set up correctly with work shown. No work shown. Delivery All problems were correct with well written explanations. Less than 2 mistakes. 2 or more mistakes. Scale: 9 100 6 85 8 95 5 80 7 90 4 75 3 70