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#1




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. 
#5




The best way to do it is write it out. If you write out "X > 8 and X > 16," you realize it looks kinda silly as opposed to (for example) "X > 8 and X < 16."
Granted, that's pretty straightforward, but you can get something a bit more involved where you write it out and realize it's redundant 
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conditional probability, soa #17 november 2001 
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