midProbability
What is the law of total probability?
Updated May 17, 2026
Short answer
It expresses total probability as a sum over conditional probabilities.
Deep explanation
The law states P(A)=Σ P(A|Bi)P(Bi), where Bi form a partition of the sample space. It is used to break complex probability problems into simpler conditional components.
Real-world example
Calculating disease probability across different age groups.
Common mistakes
- Ignoring partition completeness assumption.
Follow-up questions
- What is a partition in probability?
- How is it used in Bayes theorem?