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Q: Michael and Christine play a game where Michael selects a number from the set {1,2,3,4,....8}....

Q: Michael and Christine play a game where Michael selects a number from the set {1,2,3,4,....8}. He receives N dollars if the card selected is even; otherwise, Michael pays Christine two dollars. Determine the value of N if the game is to be fair.

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Answer:

For the game to be fair, the total expected winnings shoule be zero for the sum of both win and loss probabilities

=> Probability of winning = Prob of picking a winning number = 4/8 {2,4,6,8}

= 1/2

Probability of losing = 4/8 {1,3,5,7} = 1/2

Hence expected earnings = Prob of winning*Winnings money Prob of losing * Losing money

= 1/2*$2 + 1/2*-N = 0

= 1 = -0.5N

=> N = $2

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