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At a particular carnival, there is a dice game that costs $5 to play. -If the die lands on an odd number, you lose. -If the die lands on a 2 or 4, you win $8. -If the die lands on 6, you win $14.

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$5 How much money did you win/get back? - I did not get any of the money back How much did you pay? Did you walk away with more or less $? - I walk away losing $5

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$5 How much money did you win/get back? - I got back $8 How much did you pay? Did you walk away with more or less $? - I walk away with $3 more than I started

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$5 How much money did you win/get back? - I got back $13 How much did you pay? Did you walk away with more or less $? - I walk away with $8 more than I started

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The overall amount you walk away with (positive or negative) is called the: I walk away with $8 more than I started?

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There is a game at the fair where you pay $10 to flip a Coin once -If the coin lands heads up, you lose. -If the coin lands tails up, you win $19

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$10 How much money did you win/get back? - I did not get any of the money back How much did you pay? Did you walk away with more or less $? - I walk away losing $10

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$10 How much money did you win/get back? - I got back $19 How much did you pay? Did you walk away with more or less $? - I walk away with $9 more than I started

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If you lose, the net gain = -10

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If you win, the net gain = 9

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Have you ever wondered…….. When playing a game, your chances May seem good, but do you think That the odds are in your favor?

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Anything deal with chance such Such as a casino or lottery…. What does a business have to do to In order to be successful?

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Therefore…. At the end of the day, the business Will have a positive net gain and the players will have an overall Negative net gain

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Back to our dice example….. At a particular carnival, there is a dice game that costs $5 to play. -If the die lands on an odd number, you lose. -If the die lands on a 2 or 4, you win $8. -If the die lands on 6, you win $13.

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What could be your possible winnings? At a particular carnival, there is a dice game that costs $5 to play. -If the die lands on an odd number, you lose. -If the die lands on a 2 or 4, you win $8. -If the die lands on 6, you win $13.

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Winnings LoseWin $8 Win $13 Net Gain-5 3 8 P(X) 3/62/6 1/6 Mean = -5 (3/6) + 3 (2/6) + 8 (1/6) Mean = -2.5 + 1 + 1.33 Mean = -0.2

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Therefore, each time I play the dice game I am Expected to lose $0.20 on average. Does this seem correct that I expect to lose? Yes, because that means the business is making $

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There is a game at the fair where you pay $10 to flip a Coin once -If the coin lands heads up, you lose. -If the coin lands tails up, you win $19 Winnings LoseWin $8 Net Gain-10 9 P(X) 1/2 E(X) = -10 (1/2) + 9 (1/2) E(X) = -5 + 4.5 = -0.5

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Find the expected value if tickets are sold in a raffle at $2 each. The prize is a $1000 shopping spree at a local Mall. Assume that one ticket is purchased. Winnings LoseWin Net Gain-2 998 P(X) 1499 1500 E(X) = -2(1499/1500)+ 998(1/1500) E(X) = -1.999 + 0.665 = -1.33 _1__ 1500

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Find the expected value for example #1 if two tickets Are purchased Winnings LoseWin Net Gain-4 996 P(X) 1498 1500 E(X) = -4(1498/1500)+ 996(2/1500) E(X) = -3.995 + 1.328 = -2.67 _2__ 1500

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A lottery offers one $1000 prize, one $500 prize, and Five $100 prizes. One thousand tickets are sold at $3 each. Find the expected value of one ticket. Winnings LoseWin $1000 Net Gain-3 997 P(X) 993_ 1000 E(X) = -3(993/1000)+ 997(1/1000) + 497(1/1000) + 97(5/1000) E(X) = -2.979 + 0.997 + 0.497 + 0.485 = -1.00 _1__ 1000 Win $500 497 _1__ 1000 Win $100 97 _5__ 1000

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One thousand tickets were sold at $1 each for four Prizes of $100, $50, $25, and $10. What is the Expected value if a person purchases two tickets? Winnings LoseWin $100 Net Gain-2 98 P(X) 992_ 1000 E(X) = -1.63 _2__ 1000 Win $50 48 _2__ 1000 Win $25 23 _2__ 1000 Win $10 8 _2__ 1000

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You pay $5 to draw a card from a standard deck of 52 Cards. If you pick a red card, you win nothing. If you Get a spade, you win $5. If you get a club, you win $10. If you get the ace of clubs, you win an additional $20. Find the expected value of drawing one card. Winnings RedSpade Net Gain-5 0 P(X) 26 52 E(X) = -0.87 13 52 Club 5 12 52 Ace of Clubs 25 1_ 52

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