Law of total probability: P(A) = E(P(A|X)) (incomplete)

Dependencies: (incomplete)

1. Random variable
2. Expected value of a random variable
3. Conditioning over random variable

$\newcommand{\E}{\operatorname{E}}$ There are many results that are called 'Law of total probability'. The following is one of them.

Let $X$ be a random variable. Let $A$ be an event. Then $\Pr(A) = \E(\Pr(A|X))$.

(Requires proof)

Dependency for: None

Info:

• Depth: 7
• Number of transitive dependencies: 20

Transitive dependencies:

1. /analysis/topological-space
2. /sets-and-relations/countable-set
3. /sets-and-relations/de-morgan-laws
4. /measure-theory/lebesgue-integral
5. σ-algebra
6. Generated σ-algebra
7. Borel algebra
8. Measurable function
9. Generators of the real Borel algebra (incomplete)
10. Measure
11. σ-algebra is closed under countable intersections
12. Group
13. Ring
14. Field
15. Vector Space
16. Probability
17. Conditional probability (incomplete)
18. Random variable
19. Expected value of a random variable
20. Conditioning over random variable