I apologise in advance for what is likely a very simple question, however I have tried to find the answer on here (as well as via alt sources) and I am still struggling for a clear explanation that I can extrapolate/understand.
Here is the setup and assumptions:
Three independent trials are run (A,B,C). The expected probability of an event occurring is 0.7, 0.5 and 0.2 for trials A,B and C respectively. What is the probability that over the three trials >=1 event will occur, how is this determined and how can it be extrapolated to determine the same for N trials, each with varying event probabilities.
My understanding so far:
Trial A: P = 0.7, 1-P = 0.3
Trial B: P = 0.5, 1-P = 0.5
Trial C: P = 0.2, 1-P = 0.8
All Trials yield an Event : P = 0.7 * 0.5 * 0.2 = 0.07
No Trial yields an Event : P = 0.3 * 0.5 * 0.8 = 0.12
I know that with N independent trials of the same event probability the answer is 1-((1-P)^N) - like in the coin toss example frequently cited on here
However, I'm pretty sure in this case the answer is not 1 - 0.12 = 0.88 (i.e. 1 - cumulative P of no events across the trials)
The below post (see link) appears to answer this, however I'm still not clear on the approach and answer (and evidently not a stat guy....). Thank you in advance!