Does anyone know if there is a single formula for if the probability changes in a set manner.
I figured out the above formula while tinkering around on my own. My goal is to figure out the probability of a given even if the chances start out at 10% then increase by 5% each time, what the given chance of the event occurring at any given iteration. To begin with I started with a flat 10% chance, and figured out the above formula. Then found this while trying to check it. I used that knowledge to calculate the given chance by hand of any particular iteration, and they are as follows for iterations 1-19. (I did round most of these)
.1 .235 .388 .541 .6787 .791155 .8747 .932 .966 .9845 ..99379 .997821 .99935 .99984 .999967 .99999512 .99999951 (1 - (2.44 x 10^-8)) then 1.
I believe I calculated all these right. I got to each of them in the same manner as doing the above equation by hand over a lot of iterations. I knew that for instance the 10% repeated probability had to approach 1 asymptotically for instance. and hand calculations showed that to be true. Once I realized I was just multiplying .9 times it self for each iteration the formula was easy to devise. The one for the growing probability is not so easy. I provided the numbers so you can check any theory you come up with. Or if someone knows a proven formula that would be awesome too. I just cannot figure out any kind of elegant formula to express the change, like i could with the flat 10%. This may be stupid easy for someone on here so I figured I'd post it. I am a philosophy major, because I am too far in to change to math now. But I love mathematics which is why I am tinkering around with this. Thanks for any help you can give.