Suppose I said I had just won at craps, and I ask you what the probability of my having rolled a 4 in the first place was?

In terms of events I want
*P*(4 *first throw* | *win*),
in order to compute this we have to know
*P*(*win*) and
,
these are both directly computable, in class
I showed that:

(by the craps principle) and

Finally we have enough parts to compute: