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Math Help - Calculating probability of an event

  1. #1
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    Calculating probability of an event

    Find the probability of the following event :

    P(A \cap B | A \cup B )

    Attempt to solution :

    P(A \cap B | A \cup B )= \frac{P(A \cap B \cap A \cup B)}{P(A \cup B)}= \frac{P(A)}{P(A \cup B)}


    I don't understand how l am getting a different answer from this one ? Can someone please help me
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  2. #2
    MHF Contributor matheagle's Avatar
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    the numerator is wrong, since

    (A \cap B) \subset (A \cup B ) the intersection is the smaller set A \cap B

    and how is boris n fearless leader doing these days?

    final answer is

    P(A \cap B | A \cup B )= \frac{P(A \cap B )}{P(A \cup B)}
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