# Take out a coin! You win 4 dollars for heads, and lose 2 dollars for tails.

## Presentation on theme: "Take out a coin! You win 4 dollars for heads, and lose 2 dollars for tails."— Presentation transcript:

Take out a coin! You win 4 dollars for heads, and lose 2 dollars for tails.

How could we predict what you would win on average? Half the time, you’ll win 4 dollars. Half the time, you’ll lose 2 dollars. OutcomesHeadsTails Probability Value Total

Another way to write this: OutcomesHeadsTails Probability½½ Value4-2 Total½(4)½(-2) 1 ½(4) + ½(-2) = 1

Expected Value Since you’d win \$1 on average, it’s the value you could “expect” to win after playing over and over Expected Value: The value is what the player can expect to win or lose if they were to play a game many times.

Example 1 A die is rolled. You receive \$1 for each dot that shows. What is the expected value for the game? Outcomes123456 Probability Value Total

Example 2 A \$20 bill, two \$10 bills, three \$5 bills and four \$1 bills are placed in a bag. If a bill is chosen at random, what is the expected value for the amount chosen? Outcomes Probability Value Total

Example 3 In a game, you flip a coin twice, and record the number of heads that occur. You get 10 points for 2 heads, zero points for 1 head, and 5 points for no heads. What is the expected value for the number of points you’ll win per turn? (Hint: List every outcome.)

Example 4: Your Turn! Find the expected value (or expectation) of the games described. Mike wins \$2 if a coin toss shows heads and \$1 if it shows tails. Jane wins \$10 if a die roll shows a six, and she loses \$1 otherwise. A coin is tossed twice. Albert wins \$2 for each heads and must pay \$1 for each tails.

Mike wins \$2 if a coin toss shows heads and \$1 if it shows tails – \$1.50 Jane wins \$10 if a die roll shows a six, and she loses \$1 otherwise – \$0.83 A coin is tossed twice. Albert wins \$2 for each heads and must pay \$1 for each tails. – \$1.00 Example 4: Solutions

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