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.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.