I would like to calculate the probability of a certain result coming out at least 'x' times in 'n' attempts when the probability of result varies on every attempt; all attempts are independent events.
I found that I can use PMF when I have the same probability for every event, e.g. probability of 3 tails in 5 coin tosses. But there the probability is 50% (If we use a fair coin) for all events. When the probability changes on each attempt I'm lost.
Let's say that the probabilities of outcomes in 5 events are: 30% in the first, 35% in the second, 50% in the third, 42% for the fourth, and 25% in the fifth. What are the probabilities of it happening at least 1 in the 5, what are the probability of 2 of the 5, 3/5, 4/5 and 5/5?
I don't need the probability of the hypothetical case I'm using here as example just the formula for calculate this kind of probability or the name of this kind of thing so I can search it.