If the probability of A not appearing over a time interval is p, and the probability of B not appearing over the same time interval is q, what is the probability of both not appearing? Is it pq or p+q?
If they are independent events, multiply the probabilities.
The reason that adding is not appropriate:
-- consider this case:
-- assume that the probability of A not appearing is 0.90
-- assume that the probability of B not appearing is 0.80
-- if you added them together, you would get a probability of 1.70, an impossibilit.