See first: independence
Adaptade from CaDDiS:
Two events, A and B, are said to be conditionally independent if
(1)
Where we already have information about the situation (through our knowledge of event C), knowledge of event A will not enable us to change our estimate of the probability of event B.
e.g. The probability of me buying a hamburger and a cola, given that I am already at the snack-bar, may well just equal the chances of my feeling like eating a burger multiplied by the probability of my feeling like drinking a cola, since I am not particularly bothered about what I drink when I eat particular foods. Formally,
(2)
It does not follow that events which are conditionally independent will also be independent.
e.g. I have to walk past other shops before I reach the snack bar. Some of these shops sell cola but no burgers. If it is a hot day, I may not feel like walking all the way to the snack bar: I may just use the first shop I come to. Although I have a probability of buying a cola (depending on how much I fancy one) and a probability of buying a burger, since my choice of shop will influence the outcome, and this choice also depends on how lazy I am feeling, it will not necessarily be true that
(3)
