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Probability for Machine Learning
/Probability Rules
/Addition Rule

Addition Rule

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Addition Rule

The addition rule helps us calculate the probability of either of two events occurring. When calculating the probability of 'A or B' happening, we add their individual probabilities and subtract the probability of their overlap (to avoid counting the overlap twice).

Example: If there's a 30% chance of rain and 20% chance of wind, with a 10% chance of both occurring together, then the chance of either rain or wind is 30% + 20% - 10% = 40%.

Formally, for any two events A and B from the same sample space, the probability of their union is: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). For disjoint events where A ∩ B = ∅, this simplifies to P(A ∪ B) = P(A) + P(B). This principle extends to multiple events with the inclusion‐exclusion principle.