So I have this problem:
I am rolling a six sided die 3 times. Conditioned on the rolls all being different, what's the probability at least one die is a "1"
So I worked it out like this:
probability of not getting a 1 on the first roll is 5/6
probability of not getting a 1 on the second roll is 4/6
probability of not getting a 1 on the second roll is 3/6
I then just did (5/6) * (4/6) * (3/6) to get 60/216 possible conditions where you would not roll a 1.
Doing 216-60 you get that 158/216 possible solutions (or 13/18) possible solutions for rolling a "1" when all numbers are different. Does this make sense? The number seems a bit large and I am not sure how to check it.
Thank you in advance.