Question

What is the key word that indictes that the Addition Rule for Probabilities will be used?

Answer 1

The key word for events with probabilities that can be added is mutually exclusive.

If two events, `A` and `B`, are mutually exclusive, the probability of either one or another to happen equal to a sum their probabilities (notice different symbols used to describe logical condition `or`:
`P(A or B) = P(A+B)=P(AuuB)=P(A)+P(B)`

An explanation and intuitive justification of this rule is a similarity of a concept of probability and a concept of an area of a flat figure on a plane. Mutually exclusive events are similar to two figures on a plane that do not have any points in common. Then it's obvious that the area of both figures (the probability of one event or another) equals to a sum of areas of these two figures (equals to a sum of probabilities of individual events).