Question

How do you combine probabilities?

Answer 1

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.

`P("Heart") = 13/52 = 1/4`

`P("Jack") = 4/52 = 1/13`

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.

`P(H " or " J) = P(H) + P(J) - P(HJ)`

`= 13/52 +4/52 - 1/52 = 16/52 = 4/13`

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.

`P(H " and " J) = P(H) xx P(J)`

`=13/52 xx4/52 = 1/52`

The answer makes sense, because there is only one card that is a Heart and a Jack.