It costs $2.75 to play a dice game at the fair. The player rolls two standard dice and forms a proper fraction with the two numbers that are rolled. If the number represented by the fraction is in simplest form the player wins, if it is reducible he loses. How much should a winning roll pay out in order to make the game fair? Note: Fractions such as 2/2 are reducible to whole numbers.
A) $2.75
B) $4.50
C) $1.75
D) $5.25
E) $1.64

Question

Quizplus · Accepted Answer

There are 36 possible outcomes when rolling two standard dice. Out of these, there are 11 possible outcomes where the fraction is in simplest form (1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 2/1, 3/1, 4/1, 5/1, 6/1). Therefore, the probability of winning is 11/36, and the probability of losing is 25/36 (since there are 36 possible outcomes and 11 of them are winning outcomes).

In order for the game to be fair, the expected payout must be equal to the cost of playing ($2.75). Let's assume the winning payout is $x. The expected payout can be calculated as:
Expected Payout = (Probability of Winning * Payout for Winning) + (Probability of Losing * Payout for Losing)
$2.75 = (11/36) * x + (25/36) * 0
$2.75 = (11/36) * x
x = $4.50

Therefore, the winning payout should be $4.50 in order for the game to be fair. 
Choice B is the answer.

It Costs $2