Question

In a gambling game, you roll 2 die and if you toss 2 sixes, you win $100, otherwise you lose $5.

a. What is the chance you win?
b. What is the expected value of the game?

Answer 1

a.
`(1)/(36)` chance you win.

b. The expected value of the game is -$2.08.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

You roll 2 die and if you toss 2 sixes

For each roll, 6 possible values, 1 of which is 6. So the probability of rolling two sixes is:

`p = ((1)/(6))^2 = (1)/(36)`

a. What is the chance you win?

`(1)/(36)` chance you win.

b. What is the expected value of the game?

1/36 probability of winning 100.

35/36 probability of losing 5. So

`E = (1)/(36)*100 - (35)/(36)*5 = (100 - 175)/(36) = -(75)/(36) = -2.08`

The expected value of the game is -$2.08.