Probability of rolling 1 on a set of 6 sided dice if 1s are re-rolled once.

Question

I feel quite silly asking this (especially seeing as how this is the second time I have done so, having asked a slightly different question before), I just have seemingly forgotten all of my probability knowledge. Just to clear up what I mean it'd be rolling 3(I'd prefer to figure out how to find out this as a variable) dice with 6 sides, that re-rolls 1s once (and only once, if they are gotten again they count). The goal is to find the numerical chance of getting a 1 on any die in the set despite that. If I can figure out a way to do this with a set of dice from 1-6 dice (as in the chance for it to happen on a set with 1 die, 2 dice, 3 dice and so on) I will never have to wonder about this again.

Answer 1

See the top answer to this post: https://math.stackexchange.com/questions/470537/probability-of-rolling-at-least-one-6-while-rerolling-1s

Replacing the '6' with '1' to match your case is equivalent as long as you use fair dice.