Question

If a person rolls doubles when tossing two dice, the roller profits $90. lf the game is fair, how much should the person pay to play the game?

Answer 1

For a fair game, the person should pay `$15` to play.

Explanation:

`P("doubles")=1/6`
`color(white)("XXX")`One way to see this is to recognize that whatever
`color(white)("XXX")`value shows up on the face of the first die
`color(white)("XXX")`there is a `1/6` that that value will show up on the second die.

So on average a player can expect to win 1 roll out of each 6 attempts.

For a fair game
`color(white)("XXX")"amount to be won" xx"probability of winning" = "cost of each play"`

In this case
`color(white)("XXX")$90 xx 1/6 =$15`