Knowledge Base > Math> Probability Theory
Overview
The unconditional or prior probability corresponds to the degree of belief accorded to it in the absence of any
other information.
The conditional or posterior probability, on the other hand, associates with a degree of belief after the arrival of any
new evidence. The notation is
|
| (2.4.5) |
, which represents the conditional probability of A given that the event B has
occurred.
If event A and B are mutually exclusive, then A∩B = ∅⇒ P(A∩B) = 0 ⇒ P(A|B) = 0
On the other hand, if A is contained in B, that is, A ⊂ B ⇒ P(A∩B) = A ⇒ P(A|B) = 
.
Intuitively, if B is contained in A, B ⊂ A ⇒ P(A ∩ B) = B ⇒ P(A|B) = 
= 1
By product rule, the equation can be written as
 | (2.4.6) |
That is for a and b to be true, we need b to be true, and we also need a to be true given b.