Answer:
The expected payoff for this game is -$1.22.
Step-by-step explanation:
It is given that a pair of honest dice is rolled.
Possible outcomes for a dice = 1,2,3,4,5,6
Two dices are rolled then the total number of outcomes = 6 × 6 = 36.
The possible ways of getting a total of 7,
{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }
Number of favorable outcomes = 7
Formula for probability:
So, the possibility of getting a total of 7 =
The possible ways of getting a total of 11,
{(5,6), (6,5)}
So, the probability of getting a total of 11 = =
Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,
So, the probability of getting the sum of numbers other than 7 or 11 = =
Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,
Hence, the expected value for this game is
Therefore the expected payoff for this game is -$1.22.