P2. Conditional Probability Flashcards
1
Q
What is a conditional probability?
A
It indicates the probability of event A given we know that B has happened:
2
Q
What is Kolmogorov’s definition of conditional probability?
A
3
Q
What is De Finetti’s definition of conditional probability?
A
4
Q
What is the first revised axiom for conditional probability?
A
0 ≤ P(A|B) ≤ 1
5
Q
What is the second revised axiom for condiitonal probability?
A
P(B|B) = 1
6
Q
What is the third revised axiom for conditional probability?
A
If A1, A2, … are mutually exclusive given B, then P(A1∪A2∪…|B)=P(A1|B)+P(A2|B)+…
7
Q
What is the Law of Total Probability?
A
For any given partition {B1, B2} of Ω then for any event A:
P(A) = P(A∩B1) + P(A∩B2) = P(A|B1)P(B1) + P(A|B2)P(B2)
