Question

A dice game lets you roll 2 6 sided disc and find the sum of the numbers. A 12 wins 100 dollars, 10 or 11 wins 50 dollars, a 2 wins 3 dollars. The game costs 6 dollars to play. What is th expected outcome of this game?

Answer 1

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