Question

You are setting up to run a game of dice. The players will roll 2 dice. If the players roll a sum of 7 on the dice they earn $12, if they roll a sum of 2 or 12 they earn $36, if they rollanything else they lose. How much should you charge to have a fair game?A.$2B.$4C.$5D.$3

Answer 1

given data:

the players roll 2 dice.

if the sum of the dice is 7 then the player earn $ 12

if the sum of dice is 2 , 12 the the player earn $ 36.

to find fair game.

The possible outcome of rolling two dices are,

the total number of outcome is 36.

in that 6 have sum of 7 .

then the probablity of sum of dice is 7 is , 6/ 36.

also 2 have sum of 2, 12 .

then the probablity of sum of dice 2 is, 2/36

thus, fair game is,

$\begin{gathered} \frac{6}{36}\times12+\frac{2}{36}\times36-\frac{28}{36}x=0 \\ \frac{72+72-28x}{36}=0 \\ 28x=144 \\ x=5.14 \end{gathered}$

The answer is $ 5.