What is the law of addition in probability?

The law of addition in probability states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.

In probability theory, mutually exclusive events are events that cannot occur at the same time. For example, when flipping a coin, the events of getting heads and getting tails are mutually exclusive. The law of addition states that if A and B are mutually exclusive events, then the probability of either A or B occurring is the sum of their individual probabilities:

P(A or B) = P(A) + P(B)

This formula can be extended to more than two events. For example, if A, B, and C are mutually exclusive events, then the probability of either A, B, or C occurring is:

P(A or B or C) = P(A) + P(B) + P(C)

It is important to note that the law of addition only applies to mutually exclusive events. If events are not mutually exclusive, then the probability of both events occurring must be taken into account using the law of multiplication:

P(A and B) = P(A) x P(B|A)

where P(B|A) is the probability of event B occurring given that event A has occurred.

In summary, the law of addition in probability is a simple formula that allows us to calculate the probability of either of two or more mutually exclusive events occurring.