How do you combine probabilities?
This is quite a complex question, but here is a short explanation.
Let's us a pack of cards as an example. Single event probabilities involve only ONE aspect.
If we combine probabilities, we are considering two or more aspects.
If we ask, "What is the probability that a card is a Heart OR a jack, we are widening the options. "OR" implies ADD.
Note that we subtract the combination that is the Heart and the Jack, because that card has been counted twice.
If we ask, "What is the probability that a card is a Heart AND a jack, we are narrowing the options because we are being more specific. "AND" implies MULTIPLY.
The answer makes sense, because there is only one card that is a Heart and a Jack.