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.

(a)

To find:

Whether the game is fair or not.

Given:

Given that, a coin is tossed. The result is six and heads and you get $10 and for any other result you get $1.

Approach:

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.

E=a1p1+a2p2+...appn

Here, E is expected value, a1, a2, and an are game payouts, and p1, p2, and pn is probabilities.

Calculation:

There are six sides on a standard die, and the probability of rolling of rolling six is equal to the 16, the probability of flipping head is equal to 0.5.

To find the probability of 6 and head multiply the above both probability as shown below,

p1=(16)(12)=112

The probability other than the 1 showing is,

(b)

To find:

The payout amount if game is not fair.