The venn diagram below models probabilities of three events, a, b, and c.

By the conditional property we have:

If A and B are two events then A and B are independent if:

                               or

( since,

if two events A and B are independent then,

Now we know that:

Hence,

)

Based on the diagram that is given to us we observe that:

Region A covers two parts of the total area.

Hence, Area of Region A= 72/2=36

Hence, we have:

Also,

Region B covers two parts of the total area.

Hence, Area of Region B= 72/2=36

Hence, we have:

and A∩B covers one part of the total area.

i.e.

Area of A∩B=74/4=18

Hence, we have:

Hence, we have:

Hence, we have:

         Similarly we will have:

12/11c

or

12

c

11