You are given 8 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $ 8 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Round to the nearest cent.

To you, the expected value of the game is $0.25.

Step-by-step explanation:

Probability of rolling a sum of 8:

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

Total outcomes:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes, so .

Desired outcomes:

Sum of 8.

(2,6), (3,5), (4,4), (5,3), (6,2)

5 desired outcomes, so

Probability:

Expected value:

(5/36) probability of winning $8.

(31/36) probability of losing $1. So

To you, the expected value of the game is $0.25.

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6