Conditional probability questions arise when two possibly linked events,
and
occur. We ask, given thathas happened, what is the probability thatwill happen? The equation we use is,
the meaning of which is illustrated in the diagram below.
What we are in fact doing by saying, 'given thathas happened' is excluding the possibility thatwill not happen. The diagram above becomes restricted to the set
may still happen, and by looking at the set
the fraction of the setin whichmight still happen is the the size of the intersection divided by the size of the set
This gives us the relationship,