I use (simple) statistics/probability fairly often with a hobby of mine. I have been using Excel to calculate the answers I want, but because I don't know the proper formula, it's a tedious, messy method. I'd appreciate anyone that can explain the formula, preferably with the proper signs, for the following types of situation. In any examples provided, please list the variable used before the equation for the example.

Whenever X happens, there is a cumulative Y% chance that Z happens.

I want to be able to calculate the probability that Y has occurred if I provide a value for X.

and

Whenever W happens, there is a cumulative X% chance that Y happens. Each time Y happens, there is a cumulative Z% increase to the chance of it happening again.

I want to be able to calculate the average number of times X must occur for Y to be 100% or higher.

I am also interested in the following probability formulas. For the following three situations, you score 1 point for rolling X or higher on a die with Y number of sides and roll Z number of dice, all with Y number of sides, each time. The dice are perfectly balanced and the sides are numbered 1 to X. I want to know the likelihood of getting any given number of points on a single roll.

You score 1 point for each dice that rolls X or higher.

You score 1 point for each dice that rolls X or higher. If you roll a 1 on the die, you lose a point. If you roll the max number on the dice, you gain 2 points.

You score 1 point for each dice that rolls X or higher. If you roll a 1 on the die, you lose a point. If you roll the max number on the dice, you gain 1 point and roll that dice again.

Thank you for taking your time to help me with my hobby, your aid is much appreciated.

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