Repeated Probability
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 119. (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.
