# The Addition Rule of Probability

The Addition Rule of Probability is used to find the probability of an event A given an event B. The final solution will depend on whether the two events share elements. During the calculations, it is important to distinguish between mutually exclusive sets with elements that are equally likely to occur. A mutually exclusive set is one where no element exists in either set.

## Mutually exclusive events

The probability of two events is equal to their sum. This is known as a mutually exclusive event. An example of a mutually exclusive event is when a coin is thrown and results in either a Head or a Tail. The probability of a Head or a Tail happening is the same if the coin is thrown twice.

The Addition rule for probability is a mathematical formula that determines the probability of two mutually exclusive events. In a set of events, the element of each event must be found in at least one sample space. This element must be in either the set A or the set B in order for the probability to be equal. Then, the set A and the set B must overlap in some way. Alternatively, the two events may not be mutually exclusive.

To understand the Addition rule for probability of mutually exclusive event, we first understand what a mutually exclusive event is. Mutually exclusive events cannot happen at the same time, but they can overlap. Hence, if we want to know if two events are mutually exclusive, the probability of A plus B must be equal.

## All inclusive events

The Addition Principle describes the probability of two events occurring at the same time. When two events overlap, the probability of AB is doubled. To determine which of the two will occur, we must divide the probability of each event by the probability of the other event. If two events overlap by only one, they will have a probability of zero opposite the intersection. If they overlap by more than one, the probability of AB is doubled again.

There are other rules of probability that are derived from the addition rule for probabilities. In some cases, an event can be independently independent of the other. In this case, the probability of occurrence is 76%. However, determining the probability of a single event is not straightforward.

## Subtracting the probability of each event from the sum of both events

The probability of each event can be calculated by adding its probability to the probability of the other event. Then, if both events have a common outcome, the probability of the common event is the same as the probability of the individual event. This is called the inclusion-exclusion principle.

The probability of an event depends on its probability distribution. When two events are mutually exclusive, the probability of the intersection is zero. In this case, P(A) and P(B) will be equal. If the probability of occurrence is the same, the probability of the intersection is one. If, however, the events overlap, the probability of the overlap is the opposite of the intersection.

## Calculating the probability of each event

The probability of each event is a numerical value between 0 and 1. If a certain event occurs, then the probability of it happening is one. However, if a certain event does not happen, then the probability of it happening is zero. For example, the probability of Bill graduating from college is zero, but the probability of him not graduating is one.

This is the addition rule of probability. We can use this to find the probability of A and B. Likewise, we can also use the rule of probability to find the probability of each event separately. This rule is useful when we have to compare the probabilities of two independent events, but it is not as simple as it might seem.

When two events share the same outcome, the probability of both of them happening is equal. When you multiply the two events together, you get the total probability of all the events. However, if events J and M share the same outcome, you would have to count some outcomes twice. To correct for this, we would subtract the probabilities of each event from each other.