Question

two fair dice are tossed. The authors will pay you $12 if the dice differ, you must pay them $50 if the dice match. in the long run, how much do you expect to win per play of this game?

Answer 1

put X = amount you win. then there are two possible values for X
X = 12 or X = -50
the probability that the dice differ is 30/36 = 5/6 and the probability that they are the same is 1/6 (the same is doubles, there are six of them out of thirty six possibilities)

Answer 2

now multiply and add :

\[12 \times \frac{5}{6} - 50\times \frac{1}{6}\]
\[=\frac{60-50}{6}=\frac{10}{6}\]

Answer 3

and that is your expected value. 10/6 or
\[1\tfrac{2}{3}\] dollars a throw

Answer 4

would I lose that much or win that much

Answer 5

it is positive so you win. if it is negative you lose.

Answer 6

okay, thank you!