It is quite possible to show mutually exclusive events using Venn Diagram; two sets having no intersection that is they are disjoint.
But what about independent events? How is Venn Diagram used then? $P(A\cap B)= P(A)\cdot P(B)$. There must be intersection or overlapping of the two events $A$ & $B$.
But, then how can diagram be different from two dependent sets?
Now, if one sees the the diagram & is asked to find the probability of occurance of $A$ given $B$ has occured, he will definitely do this by $$P(A|B)= \frac{P(A\cap B)}{P(B)}$$ But $A$ & $B$ are independent events. This Venn diagram does not reflect it at all. I'm really confused how to draw a Venn diagram for independent events.
I am having a hard time in distinguishing between the difference between intersection of dependent events & intersection of independent events. Can anyone help me distinguish them?