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.

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

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

You've calculated the other probabilities correctly.

  • $\begingroup$ perfect! Makes sense, thank you! $\endgroup$ – dprogramz Jul 29 '15 at 22:49

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