A LITTLE LIGHTBULB MOMENT
Quantitative reasoning: probability, statistics and word problems
Complement Probability
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Use one minus when the opposite is easier to count.
The idea behind the cue
For any event A, P(A)=1−P(not A). The complement is everything in the sample space that is not A. This is useful when the opposite outcome is simpler to count.
Practice this flashcard →Make it memorable
Short & simple
Use one minus when the opposite is easier to count.
Acronym
CN — Clumsy Noodles.
Story
At a carnival, there are ten prize bowls and only one is clean. Counting clean bowls directly is easy here, but in harder problems you count the dirty ones instead and subtract from one whole set.
Connect the pieces
- C (Clumsy) → Complement: The event itself; use 1 minus the complement to get P(A).
- N (Noodles) → Negation: The not-A set: everything in the sample space that is not event A.
- Clumsy · Complement: The event itself; use 1 minus the complement to get P(A).
- Noodles · Negation: The not-A set: everything in the sample space that is not event A.
Know the limits
Use only when the complement is the full 'not A' set, not a different event.
Further reading · OpenStax science and mathematics textbooks ↗Check your understanding
A jar has 12 marbles. 9 are red. What is the probability of drawing a marble that is not red?
A. 1/4
B. 1/2
C. 3/4
D. 2/3
Reveal explanation
1/4
Not red is the complement of red. P(not red)=1−9/12=3/12=1/4.