25-30 ■ A Fair Game? A game of chance is described. (a) Is the game fair? (b) If the game is not fair, find the payout amount that would make the game fair.
A bag contains two silver dollars and six slugs. A game consists of reaching into the bag and drawing a coin, which you get to keep. If you draw a slug, you pay .
Whether the game is fair or not.
The total items in bags are .
The amount paid is if slug is drawn.
Fair game is game with expected value zero, if you are play a fair game many times, you would expect, on average, to break even.
To check whether the games is fair or not first calculate the expected value of event by using following formula.
Here, is expected value, , , and are game payouts, and , , and is probabilities.
There are total eight items in the bag and two of them are silver dollars. The probability of drawing the silver dollar is equal to the .
The probability of other than silver dollar is,
The payout amount if game is not fair.
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