I want to know if this is how correct way to calculate propability.

Event has 2 options, A happens or B happens. A has 0.03% chance B 99.97%. But event happens multiple times so I used this formula to calculate total chance of A happening after Y attempts.

C = 1 – (1-A) ^ Y

But every 10th event chance of A is increased to 0.045% (by 50%) and let say this chance is D but it is still same result. So here I tryed two formulas, one I called realistic and the other simplified.

Realistic:

C = 1 -(1 – A)^{9} * (1 – D) ^{1(this} is chance after 10 attempts).

Simplified (I just said it is same as if chance increased by 5% every attempt instead of 50% once in 10. So we have E = 0.0315%):

C = 1 – (1 – E) ^ 10 (again chance after 10 attempts).

Results that I got were very similar but not the same.

This event happens a lot like 10000 times so I am more interested in average chance per one event of A/D/E (same result just differnt chance) happening. So I divided previous two formulas by 10 to get average chance of A happening in event, like this:

C = (1 -(1 – A)^{9} * (1 – D) ^{1}) /10

C = (1 -(1 – E)^{10}) / 10

So basically I am where I started knowing A has 0.03% chance of happening in a event only that this A now has a bit higher chance on average because it is increased every 10th time to 0.045%.

So how correct is that and why is there a small difference in results of formula ~~I am assuming it is because of formula itself not being completely accurate as if you calculate C = 1 – (1 – 0.03)~~^{1} ~~you actually don’t get exactly 0.03 as you should but rather 0.029999997…~~

Edit: My main question would actually be can I assume in long run, on average looking at that 50% increase to 0.045% every 10th repetition is same as 5% increase to 0.0315% every repetition? Like will event happen same amount of times in those two scenarios?