Answer:
- $ 1.67
Step-by-step explanation:
Since, when two dices are rolled then the total number of possible ways = 6 × 6 = 36,
The possible ways of getting a total of 7,
{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }
So, the possibility of getting a total of 7 = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]
The possible ways of getting a total of 11,
{ (5,6), (6,5) }
So, the probability of getting a total of 11 = [tex]\frac{2}{36}[/tex] = [tex]\frac{1}{18}[/tex]
Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,
So, the probability of getting the sum of numbers other than 7 or 11 = [tex]\frac{28}{36}[/tex] = [tex]\frac{7}{9}[/tex]
Since, for the sum of 7, $ 20 will earn, for the sum of 11, $ 50 will earn while for any other total loss is $ 10,
Hence, the expected value for this game = [tex]\frac{1}{6}\times 20+\frac{1}{18}\times 50+\frac{7}{9}\times -10[/tex]
[tex]=\frac{20}{6}+\frac{50}{18}-\frac{70}{9}[/tex]
[tex]=\frac{60+50-140}{18}[/tex]
[tex]=\frac{-30}{18}[/tex]
≈ -$ 1.67
