Mutually Exclusive Events (HSC SSCE Mathematics Advanced): Flashcards

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Mutually Exclusive Events
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Mutually exclusive events definition

Events that cannot happen at same time in same experiment

Notation for mutually exclusive events AA and BB

AcapB=emptysetA cap B = emptyset

Symbol ∅\emptyset meaning

Empty set (contains no elements)

Venn diagram of mutually exclusive events appearance

Separate circles that do not overlap

Complement rule formula

P(A‾)=1−P(A)P(\overline{A}) = 1 - P(A)

Addition rule for any two events AA and BB

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)

Addition rule for mutually exclusive events

P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)

Why subtract P(A∩B)P(A \cap B) in addition rule

To avoid double-counting outcomes in both events

Value of P(A∩B)P(A \cap B) for mutually exclusive events

00 (zero)

Condition showing events are NOT mutually exclusive

A∩B≠∅A \cap B \neq \emptyset

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