Seems correct. The probability of at least one 6 is one minus the probability that both aren't a 6, which is 5/6 * 5/6 = 25/36; so the result is (36-25)/36 = 11/36.

Why wouldn't it just be the probability of either rolling at least one 6 which would be 1/6 + 1/6 = 1/3? Genuinely curious, I was never super good at probability calculations.

edit: clarification of problem.

Picture two coins and 2 flips and count the H's there (2x2) = 4 options and ((2x2) x 1/2 x 2(flips)) = 4 Heads.

HH, HT, TH, TT

However, if you count the sequences with at least one H there are (4-1) = 3 with at least 1 H (HH, HT, HT) as the HH eats up 2 H's.

Now, Picture 3 sided dice, that's (3x3) = 9 options. You will see ((3x3) x 1/3 x 2(flips)) = 6 2's.

00, 01, 02, 10, 11, 12, 20, 21, 22

However if you count there are (6 - 1) = 5 sequences with at least one 2 you get 02, 12, 20, 21, 22 as the 22 eats up an extra 2.

Now, what do you think happens with an N sided dice? What if N is 6.

PS: This seems less clear as I added more info...

Yeah doing a brute force count of the possibilities the (6,6) option is double counted by the 1/6 + 1/6 method as two distinct possibilities. Or that's what it looks like is happening. Been too long since my college combinatorics class.

Imagine doing that with 7 dice... 7/6 probability!

Which suggests the probability of the event not happening would be -1/6, which suggests the quasiprobability of the event not not happening. Obviously no ambiguity there. /s

Because those are just numbers that work. The only way to roll a 2 (for example) is to roll 2 1's - which is obviously 1/36, not 1/3.

Sorry the problem was probability of rolling at least one 6 not of rolling a 6. Edited my original to make that clearer without the original post.

Because you're not guaranteed to roll a 6, even if you roll 6 times: 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 = 100% chance? Nope. :)

Nope, you're being clever.

could you explain? I got the same thing...

I think it was meant to be a direct answer to "Am I being stupid [...]?"

Yup... shows the value of HN votes...