fair oame is one with an expected value of zero. No casino games or lotteries ar

Question

fair oame is one with an expected value of zero. No casino games or lotteries are fair games. therwise they would not turn a profit and would be unsustainable. Example 3: Instead of charging $1 for tickets in the raffle above, what should the price of a ticket be in order to make the raffle a fair game? Solution. Let the price of a ticket be SC, for some number C. Then, the gain of a winning ticket is 350-C and the gain of a Event (gain) px) losing ticket is-C. The probability distribution is shown here, -- and the equation for expected value will enable us to find C. Lose 1000 C.LoseC | 350- E(x) = o =-c(T )+(aso-o(To ). The solution to this equation is C = 0.35. So, if 35 cents is charged for each ticket, then the raffie is a fair game. Win 1000 DO IT NOW (4) 5-4.1: In the game described in the DO IT NOW problem above, how could the winnings be adjusted in order to make this a fair game with a $3.50 bet? Submit vour solutions on Rlack Board

Explanation / Answer

If we want to adjust the winning to get fair game with bet of $3.5 then Event x (gain) P(x) Lose -3.5 999/1000 Win X - 3.5 1/1000 E(x) = 0 = -3.5*(999/1000) + ((X - 3.5)/1000) So by calculating the value of X comes out to be 3500 So winning value is $3500 If we adjust probability of winnning to 1/100 then we get Event x (gain) P(x) Lose -C 99/100 Win 350 - C 1/100 E(x) = 0 = -C*(99/100) + ((350 - C)/100) So C = 3.5

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