Understanding the Addition Rule and Complement Rule for Mutually Exclusive Events in Probability

What are the two formulas for if two events are mutually exclusive?

The two formulas related to mutually exclusive events are the Addition Rule and the Complement Rule

The two formulas related to mutually exclusive events are the Addition Rule and the Complement Rule.

1. Addition Rule:
The Addition Rule states that if two events are mutually exclusive, the probability of either event happening is equal to the sum of the probabilities of each individual event. Mathematically, it can be expressed as:

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

Where:
– P(A or B) is the probability of event A or event B occurring.
– P(A) is the probability of event A occurring.
– P(B) is the probability of event B occurring.

For example, if you roll a fair six-sided die, the probability of getting either a 3 or a 5 can be calculated using the Addition Rule as follows:
P(3 or 5) = P(3) + P(5) = 1/6 + 1/6 = 1/3

2. Complement Rule:
The Complement Rule states that if two events are mutually exclusive, the probability of an event not occurring (the complement of the event) is equal to 1 minus the probability of the event occurring. Mathematically, it can be expressed as:

P(A’) = 1 – P(A)

Where:
– P(A’) is the probability of event A not occurring (the complement of A).
– P(A) is the probability of event A occurring.

For example, if you flip a fair coin, the probability of getting tails is 1/2. Therefore, the probability of not getting tails (i.e., getting heads) can be calculated using the Complement Rule as follows:
P(heads) = 1 – P(tails) = 1 – 1/2 = 1/2

These formulas are useful in determining probabilities of events when they are mutually exclusive, meaning that they cannot both occur at the same time.

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