I'm trying to figure out the crit rate of a hypothetical fighter character in DnD. I tried googling the knowledge but it keeps directing me towards sites explaining independent vs dependent probability, which I'm sure is not what I'm looking for. I'm irritated because I'm sure I learned this before in the past, but I've simply forgotten, so now I'm trying to reason through it.
In the hypothetical scenario, the fighter is attacking twice. He's rolling a D20, and a 20 is a crit. My assumption is that the 5% probability of a 20 is simply doubled to be a 10% chance of a crit. But if you think about it another way, he has a 95% chance that any attack won't be a crit, and doubling that doesn't give you a 190% of not critting, so my method is wrong.
I'm thinking it's as easy as multiplication and I'm just confusing myself for no reason, but I'm completely unsure how to go about multiplying these percentages. I can convert the 5% chance into 1.05, and Multiplying 1.05 * 1.05 gives me 1.1025, and reconverting that back into 10.25% is pretty close to my gut intuition. Conversely though, converting the Not-critting chance of 95% into 0.95 * 0.95 gives me 0.9025, or a 90.25% to not crit, or a 9.75% chance to crit, which is also pretty close to my gut intuition.
At this point, I'm thinking I'm just arranging and rearranging numbers around like an idiot without actually getting any closer to the answer to my original question. I'm positive it is staring me in the face but my boomer-ass-brain has just lost all the mathematical capability that my younger self had.