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If we have: P(A); P(B); P(A ∪ B);

And we need to compute: P(A ∩ B), P(A' ∪ B') and P(A' ∩ B).

Where ' indicates complement.

Is it correct way of doing it:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

P(A') = 1 - P(A)

P(B') = 1 - P(B)

P(A ∪ B)' = 1 - P(A ∪ B)

P(A' ∪ B') = P(A') + P(B') - P(A ∪ B)'

P(A' ∩ B) = P(B) - P(A ∩ B)

That is what I got trying to solve this question using Van Diagram...

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  • $\begingroup$ I think you got it! $\endgroup$
    – NicNic8
    Oct 12, 2014 at 5:43
  • $\begingroup$ By the way when doing such reasoning it is often helps to draw a graph and translate it to to those expressions $\endgroup$ Oct 12, 2014 at 5:52

1 Answer 1

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Yes, those look correct, though an approach using fewer steps to be based on the original three values could have given

  • $P(A \cap B) = P(A)+P(B) - P(A \cup B)$

  • $P(A' \cup B') = P(A \cap B)' = 1 - P(A)-P(B) + P(A \cup B)$

  • $P(A' \cap B) = P(A \cup B) - P(A)$

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