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.

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

addition

step-by-step explanation: