Mathematics: 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.

B, and C. Let me know if i am wrong.Step-by-step explanation:...

You are given 7 to 1 odds against rolling a sum of

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30.01.2022

The expected value of the game is $0.33.

Step-by-step 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:

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

$=[\$(7)\times \frac{6}{36}]+[\$(-1)\times \frac{30}{36}]\\\\=\frac{7}{6}-\frac{5}{6}\\\\=\frac{7-5}{6}\\\\=\frac{1}{3}\\\\=\$0.33$

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

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