Question

What is the theoretical probability of rolling a sum of 8 on one roll of two standard number cubes?

Answer 1

@mathmale @e.mccormick

Answer 2

Well, how many possible outcomes are there for rolling two dice? Then, now many of those will have a sum that is 8?

Answer 3

16, and I don't know what you mean.

Answer 4

16? It is more than 16.

Answer 5

Oh yeah, wait... 36 right?

Answer 6

If I have 0 to 9 (decimal) in 1 spot I have 10 choices. In 2 spots I have 100 choices, 00 to 99. \(100 = 10^2\) or \(choices = base^{spots}\)

Yes, \(6^2=36\)

Answer 7

Okay. And how would I find all the sums without counting them?

Answer 8

Well, a lot of times it is done on a chart. I don't know an easy mathematical way to show it. It is actually a more complex question than you might suspect. But with two dice, counting them is not that hard.

Now, if x and y \(\le6\) and \(\ge 1\), then how can \(x+y=8\)?

For example:
4+4 = 8
3+5 = 8
5+3 = 8

NOTE: 3+5 and 5+3 are different in this case. One is x=5, y=3, and the other is x=3 and y=5.

Answer 9

Okay I got 1/6 @e.mccormick

Answer 10

Did you count 4 and 4 twice? Because there is only one way to get 4 and 4.

Answer 11

Oh wups, no. Thanks

Answer 12

Actually I think I did

Answer 13

Yah. So you are off with 1/6. =)

Answer 14

You did 6 in 36. It is not 6.

Answer 15

Ok thank you, yeah :)