Addition rule
For two events, P(A or B) = P(A) + P(B) - P(A and B). You subtract the overlap because it was counted twice. The complement rule says P(not A) = 1 - P(A).
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Analogy
Two clubs have members in common. Adding both member lists counts the shared people twice, so you remove them once.
Example
P(heart) = 13/52P(king) = 4/52P(heart and king) = 1/52P(heart or king) = 13/52 + 4/52 - 1/52= 16/52 = 4/13
In practice
Used to find the chance that at least one of several things happens.
Practice
Flashcards
- What is the complement rule?P(not A) = 1 - P(A).
- What is the addition rule for two events?P(A or B) = P(A) + P(B) - P(A and B).
Questions people ask
Why do you subtract P(A and B) in the addition rule?
Outcomes in both events get counted once in P(A) and again in P(B). Subtracting the overlap once leaves each outcome counted exactly one time. In the card example, the king of hearts belongs to both groups, so it must be removed once.
What is the complement rule used for?
It is a shortcut for questions with the words at least one. Find the chance that the event never happens, then subtract from 1. The chance of at least one six in four rolls is 1 minus (5/6)^4, which is far easier than adding many cases.