Notes 13-4: Probabilities of Compound Events

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Notes 13-4: Probabilities of Compound Events We have solved these so far: P(A and B) = P(A)•P(B) Note A and B are independent events (replacement included) P(A and B) = P(A)•P(B following A) Note A and B are dependent events (no replacement, ok to use )

Alternative notation used in other textbooks (also used by IB): P(A and B) = P(A)•P(B) the “intersection” of A&B Venn Diagram: overlapping (intersecting) area of the two circles represents the overall probability.

Mutually exclusive events cannot happen at the same time Mutually exclusive events cannot happen at the same time. P(A or B) = P(A) + P(B) Alternative notation: the “union” of A&B Venn Diagram: the overall probability is the sum (or union) of the two circles.

Mutually inclusive events are where some objects can satisfy (include) the conditions of both events. P(A or B) = P(A) + P(B) – P(A and B) sum of the areas overlap Alternative notation: = P(A) + P(B) –