Probabilities of combined events

Tom Button
It is possible to construct Venn diagrams in a unit square in such a way that the areas of the regions are proportional to the probabilities and the area of the overlapping areas is the probability of the combined event. If this is done so that P(A) is a rectangle with base 1 and P(B) is a square* then the events will be independent if and only if the overlapping area is a similar rectangle to the rectangle representing P(B). The diagonal on the diagram helps visualise when the rectangles are similar. An alternative way of looking at this is to identify if the fraction of the square for P(B) that is shaded twice is the same fraction of the whole square that is shaded for PA). *If A and B are independent it will be possible to draw P(B) as a square; however, for some other values of P(A∩B) it may not be possible to satisfy all the conditions and draw P(B) as a square.