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Math Help - Problem with equation of independent events

  1. #1
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    Problem with equation of independent events

    Please explain the question posted in the file attached.

    CB
    Attached Thumbnails Attached Thumbnails Problem with equation of independent events-untitled.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by computer-bot View Post
    Please explain the question posted in the file attached.

    CB
    A \cap B is the set of simple events which are in both A and B, and |A \cap B| is the number of elements in this set.

    It is the number of ways the both A and B can simultaneously occur.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    A \cap B is the set of simple events which are in both A and B, and |A \cap B| is the number of elements in this set.

    It is the number of ways the both A and B can simultaneously occur.

    RonL
    CaptainBlack I know what does A intersection B means but what I don't understand is that what does this statement |A and B|/|B| has to do with the occurence of two events. I mean the author said that "The probability that A occurs is P(A) = |A|/6 = 3/6 = 1/2, while presuming B occurs, the probability that A occurs is |A and B|/|B|. What I am trying to understand is that how did the author form this equation for this situation. I hope my question is clear.
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  4. #4
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    The probability of A happening given that B has occurred in symbols is
    P(A|B) = \frac{{P\left( {A \cap B} \right)}}{{P(B)}}.
    That explains the intersection in your question.

    Thus if A and B are independent that means that
    P(A|B) = \frac{{P\left( {A \cap B} \right)}}{{P(B)}} = P(A)\quad  \Rightarrow \quad P\left( {A \cap B} \right) = P(A)P(B).
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