CONDITIONAL PROBABILITIES
A probability P(A) ("probability of A") is a number between 0 (impossible)
and 1 (certain) which describes how likely a given event 'A' may be.
e.g. P(Correctly matching a number randomly chosen between 0 and 49)=1/50.
A conditional probability P(A|B) ("probability of A given B") is a
probability where the chance of the event A happening is affected by some
other property B.
e.g. The chances of winning the national lottery will clearly be affected
by the number of different combinations which you purchase:
P(You winning the national lottery | You have bought 2 tickets)
will be less than
P(You winning the national lottery | You have bought 100 tickets).
In some cases, conditional probabilities can be easy:
P(You winning the national lottery | You have bought no tickets)=0
!
Conditional probabilities can be manipulated using Bayes's
Theorem, and can be calculated using the chain
rule. In the topic of Bayesian Belief networks, the concept of Conditional
Independence is particularly important.