Conditional
Probability of event A conditioned on the fact that event B has happened is called the conditional probability and written as P(AIB).
P(AIB)=Probability Both A and B happens/ Probability B happens.
Example:
A six-sided die with faces from 1 to 6 is rolled twice. What is the probability that the face 5 turned up on first try given that the sum of the two faces is 9?
P(sum of faces is 9)=4/36=1/9.
P(face 5 turns up on the first try and sum is 9)=(1/6)*(1/6)=1/36.
P(face 5 turned up on first try given sum is 9)=(1/36)*(1/9)=1/4.