Expected values of games

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Expected values of games You decide to buy a $2 Powerball ticket when you hear that the prize is $100,000,000. What is the expected value of this “game”? Rules Pick 5 “white” numbers out of 60 possible values. No numbers are repeated. Pick one “red” number from 35 possible values. 5 correct 1 correct 4 correct 3 correct 0 correct All others $100,000,000 $200,000 $10,000 $100 $7 $4 $3 -$2

Discrete Math Section 16.6 Find the expected value of a game In 100 spins the expected outcome is: 25($1) + 25($3) + 25 ($5) + 25 (-$10) = -$25 You could expect to lose $25 after having played 100 times The values $1, $3, $5, and -$10 are called the payoff. -$25 is the expected value of the game

The expected value of a game is calculated by: If the expected value is zero, the game is fair. Expected value = x1 ∙ P(x1) + x2 ∙ P(x2) + … xn ∙ P(xn)

Example Two coins are tossed. If both land heads up, then player A wins $4 from player B. If exactly one coin lands heads up, then player B wins $1 from A. If both land tails up, then B wins $2 from A. Is this a fair game?

Page 635 problem 19 Event Bid accepted Bid denied Payoff Probability

Assignment Page 633 Problems 2,4,6,8,9,11,14,17,18,20,22,24