Answer:
Step-by-step explanation:
A two 6 sided die is rolled
Sample space would be (1,1)...(1,6)....(6,1)....(6,6)
Let x be the sum obtained
X can take values as 2 or 3 ....12
P(x=12) = P(6,6) =1/36
P(x=10 or 11) = P{(5,5)(5,6) (6,5) (4,6)(6,4)}=5/36
P(2) =P(1,1) = 1/36
For other outcomes no payment
Thus we can list this as
Sum 2 3 4 5 6 7 8 9 10 or 11 12
Prob 1/36 5/36 1/36
Gain 3 0 0 0 0 0 0 0 50 100
E(gain) 3/36 0 0 0 0 0 0 0 250/36 100/36
E(gain) = total= 353/36
Cost of game = 6
E(outcome) = E(gain -6) = E(gain)-6 = 353/36 -6
= 3.806
