[addisonl]

> Question: A fair die rolling a 6 twice in a row is more likely than rolling 1-2-3-4-5-6 in sequence

Two 6s in a row is 1/36 chance (1/6)^2

1-2-3-4-5-6 is a 1/46656 chance (1/6)^6

Website is claiming they are the same probability:

> Same probability: 1/46,656 — Both outcomes have exactly the same probability: (1/6)^6 = 1/46,656. This illustrates the representativeness heuristic — random-looking sequences feel more probable than ordered ones.

Website's "answer" is wrong: was the question supposed to be rolling a 6 six times in a row?

[cyanydeez]

Yeah, most likely it was try to identify a bias of human perception, that 1,2,3,4,5,6 would be more probably than 6x6.

A better way to illustrate this bias is with coin flips. People will tell you that odds of 6 heads is more rare than the odds 3 tails then 3 heads. The difficulty is understanding whether they mean "in order" or "as a group".

If it's in order, the odds are the same. Every order of H/T has the same probability, but humans will see "all heads" and think that's more rare. But the important bit is whether there's a clear understanding ordering.

[convexly]

That's definitely better framing for this question. Much cleaner way to illustrate that point!

[convexly]

You're right, that's a mistake in how I phrased the question. It should say "six times in a row" not "twice in a row". Fixing it now! Thanks for pointing that out!

[snarf21]

If anyone is interested in why we are bad at estimating, please check out the amazing book Thinking, Fast and Slow: Daniel Kahneman.

[convexly]

Great recommendation. That was one of the biggest influences for starting to write my decisions down and then building this.

[1qaboutecs]

came with the same complaint. the website then had the nerve to tell me i am overconfident.

[convexly]

Fair point! Bad question on my end. The overconfidence was based on all 10 questions though, not just that one!