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?

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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?

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Answer 1 · 2017-09-03T12:08:39

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

Explanation:

$P (doubles) = \frac{1}{6}$ $P("doubles")=1/6$
$XXX$ $color(white)("XXX")$ One way to see this is to recognize that whatever
$XXX$ $color(white)("XXX")$ value shows up on the face of the first die
$XXX$ $color(white)("XXX")$ there is a $\frac{1}{6}$ $1/6$ 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
$XXX amount to be won \times probability of winning = cost of each play$ $color(white)("XXX")"amount to be won" xx"probability of winning" = "cost of each play"$

In this case
$XXX $ 90 \times \frac{1}{6} = $ 15$ $color(white)("XXX")$90 xx 1/6 =$15$

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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?

1 Answer

Explanation:

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