What are mutually exclusive events?

Data Science, AI and ML
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#1

Mutually exclusive events are the events that cannot occur or happen at the same time. In other words, the probability of the events happening at the same time is zero.

Mutually exclusive events are events that cannot occur or happen at the same time. The occurrence of mutually exclusive events at the same time is 0. If A and B are two mutually exclusive events in math, the probability of them both happening together is: P(A and B) = 0. The formula for calculating the probability of two mutually exclusive events is given below:

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

Some of the examples of the mutually exclusive events are:

  • When tossing a coin, the event of getting head and tail are mutually exclusive events. Because the probability of getting head and tail simultaneously is 0.
  • In a six-sided die, the events “2” and “5” are mutually exclusive events. We cannot get both events 2 and 5 at the same time when we threw one die.
  • In a deck of 52 cards, drawing a red card and drawing a club are mutually exclusive events because all the clubs are black.

From the definition of mutually exclusive events, the following rules for probability can be concluded.

  • Addition Rule: P (A + B) = 1
  • Subtraction Rule: P (A U B)’ = 0
  • Multiplication Rule: P (A ∩ B) = 0