suppose there is a probability x that an event happens (and clearly 1-x it doesn't). The catch is, x is not constant, it depends on how many times x has happened before. In other words, with a probability x, the event happens and x increases. With a probability 1-x, the event doesn't happen, and x remains the same. Hence the probability of the event happening increases in how many times the event has happened.

I know this isn't a lot of detail. I am just looking for a suggestion of how to begin modelling something like this. I don't know where to even start. Does anybody have any quick comments about where I should look?

Thank you very much,

Nick