I'm trying to come up with a pure statistical probability of overlap for 3 non-exclusive groups by using Independence, so $P(A\cap B) = P(A)P(B)$
All groups make up part of the whole, but again, are non-exclusive, and the whole does not need to be fully represented by the sum of the 3 groups.
Group $A$ makes up 66% of the whole.
Group $B$ makes up 31% of the whole.
Group $C$ makes up 20% of the whole.
So I'm calculating a 20% probability of overlap Between $A$ and $B$, a 6% probability of $B$ and $C$, and a 13% probability of $A$ and $C$.
Am I doing the math correctly? What would be the way to figure out the probability of a 3 way overlap? Is it possible? Thank you.