Module 2 · Probability Foundations · Topic 4

Addition Rule

Mutually Exclusive Events. If A and B cannot happen at the same time (mutually exclusive), then P(A ∩ B) = 0, and the formula simplifies to P(A ∪ B) = P(A) + P(B).

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Key formulas

General Addition Rule

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

From the Probability Foundations formula sheet

Conditional Probability: P(A | B) = P(A and B) / P(B) — Probability of A after restricting attention to cases where B occurred.
Bayes' Theorem: P(A | B) = P(B | A)P(A) / P(B) — Updates a prior probability after observing evidence.

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Worked example

Worked Example

Drawing a card: P(king or heart) = P(king) + P(heart) − P(king of hearts) = 4/52 + 13/52 − 1/52 = 16/52 ≈ 0.308.

When to use it

Avoiding Double-Counting

We subtract P(A ∩ B) because outcomes in both A and B are counted twice when we add P(A) and P(B). Always check if events overlap.

Related glossary terms

Independence: Two events are independent when one occurring does not change the probability of the other. Example: Two separate fair coin flips are independent.

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