Algebra 2 · Unit 11 · Topic 11.3
Complements and Unions of Events
Probabilities lie from 0 to 1.
Definition and explanation
Probabilities lie from 0 to 1. The complement rule is P(not A) = 1 − P(A), and the union rule is P(A or B) = P(A) + P(B) − P(A and B). Counting favorable outcomes over total outcomes assumes equally likely outcomes.
Worked example
Roll a fair six-sided die. Let A mean an even result and B mean a result greater than 4. Their probabilities are 3/6 and 2/6, with overlap {6} of probability 1/6. Thus P(A or B) = 4/6 = 2/3.
Common mistake
Adding event probabilities without subtracting overlap double-counts outcomes shared by both events.
Key takeaway
Probabilities lie from 0 to 1.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.