Applied Mathematics

Probability Theory

What are the addition rules of probability?

In probability theory, the addition rule is used to determine the probability of events A or B occurring. The notation is most commonly seen in terms of sets: P(AB) = P(A) + P(B) - P(AB), in which P(A) represents the probability that event A will occur, P(B) represents the probability that event B will occur, and P(AB) is translated as the probability that event A or event B will occur. For example, if we wanted to find the probability of drawing a queen (A) or a diamond (B) from a card deck in a single draw, and since we know there are 4 queens and 13 diamond cards in the deck of 52, the equation and resulting probability becomes: 4/52 + 13/52 - 1/52 = 16/52 (the 1/52 is derived by multiplying 4/52 × 13/52).

But there are also rules of addition for mutually exclusive and independent events. For mutually exclusive events, or events that can’t occur together, the addition rule reduces to P(AB) = P(A) + P(B). For independent events, or those that have no influence on each other, the addition rule reduces to P(AB) = P(A) + P(B) - P(A) | P(B).


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