Question

600 chances are sold at ​$2 apiece for a raffle. There is a grand prize of ​$400​, two second prizes of ​$250​, and five third prizes of ​$150. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not​ fair, determine a price for playing the game that would make it fair. The expected value of the game is ​$ ?.

Answer 1

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1.

The expected value of the lottery

= Prize win - cost per raffle

= (1/600)*(400) + (2/600)*(250) + (5/600)*150 - $2

= $0.75

2. The game will be fair if expected value of lottery =0

Here it is $0.75, so it not zero, hence this is not a fair game

Answer: This is not a fair game

3. To make the game fair therefore the person should pay $0.75

Answer: A price for playing the game that would make it fair: $0.75

4. We calculated this as $0.75 in part a)

Answer: Expected value of this game: $0.75