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What Are Disjoint Events in Probability?

Theory

Disjoint Events

Disjoint events are events that never occur together. Two events A and B are disjoint if the intersection of the sets is empty. Mathematically, this is written as

P (A B) = 0  because A B = no elements.

P (A B) = 0 because A B = no elements.

Disjoint events

Example 1

You roll a die. Let A be the compound event defined as “more than four dots”, A = {5, 6}, and B be “fewer than three dots”, B = {1, 2}. That means the intersection between A and B is the empty set, because they have no outcomes in common. They can never both occur at once.

You denote the empty set with the symbol .

Note! Complementary outcomes are always disjoint, because an event can not both happen and not happen at the same time.

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