SOLUTION: In a game of change if you purchase one ticket out of the 100 tickets being sold at a cost of $5.00 how much money would you expect to win taking into consideration the cost of the

Question 479070: In a game of change if you purchase one ticket out of the 100 tickets being sold at a cost of $5.00 how much money would you expect to win taking into consideration the cost of the ticket. The winning prize is $500?
If I purchase two tickets instead of one ticket at the same cost of $5.00 each, how much money would I expect to win, taking into consideration the cost of the tickets if the winning prize is $500.
Which of these games, if any, are fair?
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a game of chance if you purchase one ticket out of the 100 tickets being sold at a cost of $5.00 how much money would you expect to win taking into consideration the cost of the ticket. The winning prize is $500?
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E(gain) = (1/100)495 + (99/100)(-5) = (495-495)/100 = 0
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If I purchase two tickets instead of one ticket at the same cost of $5.00 each, how much money would I expect to win, taking into consideration the cost of the tickets if the winning prize is $500.
E(gain) = (2/100)490 +(98/100)(-10) = (980 - 980)/100 = 0
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Which of these games, if any, are fair?
Ans: Both are fair.
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Cheers,
Stan H.
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Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
let x= random variable for the earnings
If only one ticket is bought,
If x = -5, then p(x) = 99/100,
If x = 495, then p(x) = 1/100, and so
E(x) = -5*(99/100) + 495*(1/100) = 0, the expected earning.
If 2 tickets are bought,
E(X) = -10*(98/100) + 490*(2/100) = 0, the expected earning.
Both games are fair.
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