Question

The probabilities for each event are given by the ratio of the area of the event to the total area of 72. For example, Event C is Red Only. So, for the probability of Event C, you have: P(C)=area of red/total area=18/12x6=18/72=1/4=0.25 Are A and B dependent or independent events? Use conditional probabilities to support your conclusion.

Answer 1

Let say that you want to take 1 area. Before the event, the probability of A and B would be:
A= blue and green=  (18/12x6) + (18/12x6) = 36/72
B= green and yellow= (18/12x6) + (18/12x6) = 36/72

If the area that picked is green, then the probability of A and B become
A= blue and green= (18/12x6-1) + (17/12x6-1) = 35/71
B= green and yellow= (17/12x6-1) + (18/12x6-1) = 35/71

Both of the areas of A and B is decreased because they share the probability of green. So A and B would be a dependent event.