Probability

At GCSE you extend probability to include Venn diagrams with set notation, conditional probability, frequency trees, and independent versus mutually exclusive events.

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Probability Fundamentals (Review)

P(event) = favourable outcomes / total equally-likely outcomes

P(not A) = 1 − P(A)

For mutually exclusive events: P(A or B) = P(A) + P(B) For independent events: P(A and B) = P(A) × P(B)

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Venn Diagrams and Set Notation

Notation	Meaning
A ∩ B	A intersection B — in BOTH A and B
A ∪ B	A union B — in A OR B (or both)
A'	Complement of A — NOT in A
n(A)	The number of elements in set A

Addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)