Question

You are given 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice, meaning you win $7 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.

Answer 1

The expected value of the game is $0.33.

Explanation:

There are N = 36 outcomes of rolling two 6-sided fair dice.

The sample for the sum of two numbers to be 7 is:

S = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)}

n (S) = 6

It is provided that there is a 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice.

That is, you win $7 if you succeed and you lose $1 if you fail.

Compute the expected value of the game as follows:

`E(X)=\sum x\cdot P (X=x)`

`=[\$(7)* (6)/(36)]+[\$(-1)* (30)/(36)]\\\\=(7)/(6)-(5)/(6)\\\\=(7-5)/(6)\\\\=(1)/(3)\\\\=\$0.33`

Thus, the expected value of the game is $0.33.