Question

What is the answer to this problem?

1 .You roll two, fair, EIGHT SIDED dice (i.e. they each have faces giving 1, 2, 3, 4, 5, 6, 7 or 8).
a. List all the possible sums of the two dice and how many ways each sum can happen.
b. From the total number of possible sums and the number of ways each sum can
happen, calculate the probability of getting each sum, listing it both as a fraction and as a percentage.

Answer 1

See below:

Explanation:

We can chart it out:

`((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6,ul7,ul8),(1|,2,3,4,5,6,7,8,9),(2|,3,4,5,6,7,8,9,10),(3|,4,5,6,7,8,9,10,11),(4|,5,6,7,8,9,10,11,12),(5|,6,7,8,9,10,11,12,13),(6|,7,8,9,10,11,12,13,14),(7|,8,9,10,11,12,13,14,15),(8|,9,10,11,12,13,14,15,16))`

There are 64 different rolls possible. The sums, number of ways to achieve those sums, and the probabilities of getting them are:

`(("Sum","Ways","Fraction","Percentage"),(2,1,1/64,1.56%),(3,2,1/32,3.13%),(4,3,3/64,4.69%),(5,4,1/16,6.25%),(6,5,5/64,7.81%),(7,6,3/32,9.38%),(8,7,7/64,10.94%),(9,8,1/8,12.50%),(10,7,7/64,10.94%),(11,6,3/32,9.38%),(12,5,5/64,7.81%),(13,4,1/16,6.25%),(14,3,3/64,4.69%),(15,2,1/32,3.13%),(16,1,1/64,1.56%))`