I'm playing one game and the following event is presented to me:
66% of bad event happening
33% of good event happening
I saved the game just before this event fires, and I'm reloading the game for already some time trying to get the 33% chance of good event to happen, however it always happens bad which has 66% chance of happening.
The bad event is too bad to get over it, otherwise I wouldn't bother with this...
What are my actual chances expressed in percentages of good event to happen? How many times on average will I have to reload a game for good event to happen?
Let $X$ be the random variable that counts the number of times you reload the save. You want the average number of times you reload until you get the good event. The good event happens with probability $p = \frac{1}{3}.$ The scenario described follows the geometric distribution with mean $3.$
Note that an average of $3$ reloaded saves until good does not mean reloading three times will always give the good event. It may also be the case that the event is already saved to memory when you saved your file, so you're stuck with what comes.