My problem revolves around an event that has a certain probability of failing. You get X attempts and your prize depends on your successes. Using this question I found here: Probability of rolling 3 sixes in 6 rolls I was able to get this far. In my example though, I have two events, with different probabilities of failing, with a different number of attempts made. I am trying to calculate the average outcome and am not sure what comes next.
Event A has a 38% chance of failing. The event happens twice. The chance of one success is 86%, the chance of two successes 39%(with rounding). A success on A is worth $10.50.
Event B has a 43% chance of failing. The event happens twice. The chance of one success is 82%, the chance of two successes is 33% (with rounding). A success on B is worth $7.50.
That leaves the following possible results: A, B, AA, AB, BB, AAB, ABB, AABB
I'm not sure how to calculate the possibilities of each of these happening, or how to calculate the average amount of money. Thanks.