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Thread: Quick probability proof

  1. #1
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    Quick probability proof

    Let A and B be two events. Prove that $\displaystyle P(AB) \geq P(A) + P(B) - 1$
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    Quote Originally Posted by Zennie View Post
    Let A and B be two events. Prove that $\displaystyle P(AB) \geq P(A) + P(B) - 1$
    Assuming $\displaystyle P(AB)$ means $\displaystyle P(A\cup B)$, use that $\displaystyle P(A\cup B) = P(A) + P(B) - P(A \cap B)$ and that $\displaystyle 0\le P(X) \le1$ for any event $\displaystyle \,X$.
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    Sorry for the lack of clarity.

    $\displaystyle P(AB)$ means $\displaystyle P(A \cap B)$. So prove that $\displaystyle P(A \cap B) \geq P(A) + P(B) - 1$
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    Quote Originally Posted by Zennie View Post
    Sorry for the lack of clarity.

    $\displaystyle P(AB)$ means $\displaystyle P(A \cap B)$. So prove that $\displaystyle P(A \cap B) \geq P(A) + P(B) - 1$
    If you solve for $\displaystyle P(A \cap B)$ you'll see it works out the same.
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