Imagine there are two types of boxes, , that only contain white balls (), and , that contain one white balls and twelve black (incidentally, just to be precise, although the detail is absolutely irrelevant, we have to infer from Columbo's words, ``You didn't touch any of these twelve cameras. You picked up that one'', the cameras were thirteen).
You take at random a box and extract a ball.
The resulting color is
You might be interested to evaluate
the probability that the box is of type ,
in the sense of stating in a quantitative way
how much you believe
In formal terms we are interested in
, a problem that can be sketched as
A typical mistake at this point is to confuse with , or, more often, with , as largely discussed in Ref. . Hence we need to learn how to turn properly into using the rules of probability theory.