If a player rolls two dice and gets a sum of 2 or 12, she wins $50. If the person gets 4 or 8, she wins $5. The cost to play the game is $1. Find the expectation of the game.

Question

if the person sum is odd she wins $10

Answer 1

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

The chart above shows the possibilities for the total when rolling two dice. I am unable to draw a vertical line to isolate the first column

There is one ways to get 2 , there is one way to get 12

There are three ways to get 4, there are 5 ways to get 8

There are 18 ways to get an odd total.

The expected value is (50)(1+1)/36+5(3+5)/36+10(18)/36-1=320/36-1=7 8/9