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What are Mutually Exclusive Events?
Mutually Exclusive Events – Infinity Learn: Mutually exclusive events are events that cannot happen at the same time. For example, flipping a coin and getting heads is a mutually exclusive event to flipping a coin and getting tails.
Mutually Exclusive Event Definition
A mutually exclusive event is an event that cannot happen simultaneously with any other event. In other words, if two events are mutually exclusive, then the occurrence of one event precludes the occurrence of the other.
If X and Y happens to be mutually exclusive, then (X n Y) = 0
Mutually exclusive events are events that cannot happen at the same time. For example, rolling a 1 on a die and rolling a 2 on a die are mutually exclusive events, because they cannot happen at the same time
Mutually exclusive Events Examples
1) Rolling a six on a die
2) Drawing a king from a deck of cards
In both cases, there are only six possible outcomes, and only one of those outcomes can happen at a time.
Rules for the probability of the mutually exclusive events
- In probability theory, the probability of two mutually exclusive events happening is the sum of their individual probabilities. For example, the probability of rolling a two on a six-sided die and rolling a four on a six-sided die is 1/6 + 1/6 = 2/6 = 1/3.
- This rule can be generalized to any number of mutually exclusive events. The probability of any one of these events happening is the sum of the probabilities of the individual events that make it up.
Mutually Exclusive Events Formulas
There are three formulas for mutually exclusive events:
1) The probability of all events occurring is the sum of the individual probabilities of each event occurring:
P(A and B) = P(A) + P(B)
2) The probability of at least one event occurring is the sum of the individual probabilities of each event occurring, minus the probability of both events not occurring:
P(at least one event) = P(A) + P(B) – P(A and B)
3) The probability of no events occurring is the product of the individual probabilities of each event not occurring:
P(no events) = P(A) x P(B)
