The idea

Mutually exclusive and independent events

The two key relationships between events: mutually exclusive (they cannot both happen, so P(A∩B) = 0 and P(A∪B) = P(A) + P(B)) and independent (one does not affect the other, so P(A∩B) = P(A)×P(B)). How to use each rule, how to TEST whether two events are independent, and why mutually exclusive and independent are not the same thing.

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Statistics · Probability

Mutually exclusive and independent events

Why it works

Two different relationships, two different rules

Half the marks in probability hinge on two words that sound interchangeable and aren't. Mutually exclusive events cannot both happen at once — rolling a

2

and rolling a

5

on one die, say. Their circles on a Venn diagram do not overlap, so

P(A \cap B) = 0, \qquad \text{and therefore} \qquad P(A \cup B) = P(A) + P(B).

The addition formula loses its

-P(A\cap B)

term because there is no overlap to double-count.

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