Conditional Probability
In general if P(A)>0, then P(BA) = P(A and B)/P(A).
Sometimes, as in the case of SOA #17 from November 2001: The loss due to a fire in a commercial building is modeled by a random variable X with density function f(x) =.005(20x) for 0<x<20
Given that a fire loss exceeds 8, what is the probability that it exceeds 16?
That conditional probability is shortened to P(BA) =P(AandB)/P(A) = P(B)/P(A).
What is this due to? Why does it sometimes get reduced to this and other times not?
Thank you.
