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 die is rolled, and a coin is tossed. If the result is a "six" and "heads," you get $10. For any other result you pay $1.
Whether the game is fair or not.
Given that, you get if a one or a six shows otherwise you pay .
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 six sides on a standard die, and the probability of a six or showing is equal to .
The probability other than the six or showing is,
The payout amount if game is not fair.
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