Say I'm playing a game and I get to roll $5$ dice once. If I roll $3$ or more sixes I lose. If I roll at least $1$ one I lose. I can lose if both losing conditions happen at the same time too. If I don't lose, I win. What is the probability that I win?
I attempted to figure this out by calculating the possible individual losing conditions and summing them together. But I think I had some overlap since I got $\sim43\%$ but when simulated with $20,000$ rolls in excel the win rate was $\sim38\%$.