## 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(*A*∪*B*) = P(*A*) + P(*B*) - P(*A*∩*B*), in which P(*A*) represents the probability that event *A* will occur, P(*B*) represents the probability that event *B* will occur, and P(*A*∪*B*) 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(*A*∪*B*) = P(*A*) + P(*B*). For independent events, or those that have no influence on each other, the addition rule reduces to P(*A*∪*B*) = P(*A*) + P(*B*) - P(*A*) | P(*B*).