[laddng]

"If you roll 2 six-sided dice, what are the chances you roll at least one dice above 5 (5 or 6)?"

A nice trick to visually solve this in your head I heard once is:

If you think of rolling two dice as a square. X and Y are each dice. You get a 36 square board. Getting 1 six is just the upper boarder. 6 on the top, 6 on the right (6 and 6 overlap). So 11 out of the 36 squares.

[borishn]

Chances of rolling below 5 are 4x4/36 = 16/36, so above are 20/36

And here is the board: https://www.edcollins.com/backgammon/diceprob.htm

[astatine]

There is the small matter of "equal to 5"

[will_pseudonym]

Another way to think about it using the square board concept would be to figure out how many ways you can get not the result you're looking for, and take 36 minus that number for the number of possible squares out of 36 squares. So getting "no 6's" on either die would be the square on the board of 1 through 5, by 1 through 5, or 25 squares. So inverting that we'd arrive at the 11 squares.

In studying probability, I found that accounting for the "overlap" as you described it was more tedious in more complicated problems than just always calculating the joint probabilities and inverting them.