My question is related to my job and asking to learn.
Simplified case is:
Event A and Event B failure rates are exponentially distributed.
Event A (failure of item A) => failure rate (lambda): 0,0002
Event B (failure of item A) => failure rate (lambda): 0,0008
for a duration of 500.
I want to understand the probability that both events occurs but event A occurs before event B.
Event A and B are independent. One does not trigger (not change the prob.) the other.
I made 200,000 trials monte carlo sim. and get 0,01533 for probability that both events occurs but event A occurs before event B.
Q1) But where is this coming from? What is the analytical solution for this case?
Q2) Which specific statistics topic should I read on web if the number of sequential items increases and the problem gets more complex?