we calculate Expected Value by multiplying each outcome by the probability of that outcome, then adding up the products.

First Outcome: win $(10-1) = $9

First Event: sum of 2 and 12 comes up

P(Fist Event) = 1/36 + 1/36 = 2/36 = 1/18

Second Outcome: lose $1

Second Event: sum of 2 and sum of 12 does not come up

P(Second Event) = 1 - 1/18 = 17/18

Expected Value = 9*(1/18) - 1(17/18) = (9 - 17)/18 = - 8/18 = - 4/9 = - 0.444

The expected value of playing the game is -0.444.

we calculate Expected Value by multiplying each outcome by the probability of that outcome, then adding up the products.

First Outcome: win $(10-1) = $9

First Event: sum of 2 and 12 comes up

P(Fist Event) = 1/36 * 1/36 = 1/36*36

Second Outcome: lose $1

Second Event: sum of 2 and sum of 12 does not come up

P(Second Event) = 1 - 1/(36*36) = (36*36-1)/(36*36)

Expected Value = 9*(1/(36*36)) - 1*(36*36-1)/(36*36)= - 13/18 = - 0.992

The expected value of playing the game is -0.992.