# Am I properly calculating this probability?

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.

• Are $A$, $B$ and $C$ all independent? – David Quinn Jul 29 '15 at 19:40
• They can overlap but are independent. – dprogramz Jul 29 '15 at 22:48

We have $$P(A \cap B \cap C)=P(A \cap (B \cap C)) = P(A)P(B \cap C)=P(A)P(B)P(C)$$