I find venn diagram and table are conflicting in terms of illustrate joint probability (table for discrete case).
Let's say for the following example:
We know that the joint probability of X and Y is the area of intersection X and Y over the total area.
Now let's say the following table describes the joint probability of X and Y as well:
They are apparently conflicting because in the venn diagram there will always be a value of X, if given, the probability of Y is 0, since there is always a portion of X does not overlap with Y.
Because of this I have problem of understanding concept such as P(A|E1)+P(A|E2)+...=1. It is used in the proof for the concept in this post:Proof that conditional probabilities sum up to one
Since joint probability is well-defined on a venn diagram it is supposed to make sense.