# 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.

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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.

\$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

\$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

\$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

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

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

\$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

\$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

If you lose, the net gain = -10

If you win, the net gain = 9

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

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

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

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.

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.

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

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 \$

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

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

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

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

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

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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