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.

what do u need to know

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.