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Math Help - Probability of the Union of 4 events

  1. #1
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    Probability of the Union of 4 events

    What is the probability of the union of 4 events? The events are:

    E- hitting an even number on a dartboard= .0249

    D- hitting a double P=.1049

    N- hitting a number higher than 10 P=.0249

    B- hitting a bullseye P= .007

    I came up with:

    1. P(E)+P(D)+P(N)+P(B) -


    2. [P (E \cap D) + P(E \cap N) +P (E \cap B) + P(D \cap N) + P(D \cap B +[P(N \cap B] +

    3. P(E \cap D \cap N)]+ P(D \cap N \cap B)] -


    4. P( E \cap D \cap N \cap B)


    I'm basically asking if I got the formula right for the probability of the union of 4 events.


    Any help is appreciated
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  2. #2
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    Quote Originally Posted by divinelogos View Post
    What is the probability of the union of 4 events? The events are:

    E- hitting an even number on a dartboard= .0249

    D- hitting a double P=.1049

    N- hitting a number higher than 10 P=.0249

    B- hitting a bullseye P= .007

    I came up with:

    1. P(E)+P(D)+P(N)+P(B) -


    2. [P (E \cap D) + P(E \cap N) +P (E \cap B) + P(D \cap N) + P(D \cap B +[P(N \cap B] +

    3. P(E \cap D \cap N)]+ P(D \cap N \cap B)] -


    4. P( E \cap D \cap N \cap B)


    I'm basically asking if I got the formula right for the probability of the union of 4 events.


    Any help is appreciated
    \displaystyle P(A\cup B\cup C\cup D)=P(A)+P(B)+P(C)+P(D)-P(A\cap B)-P(A\cap C)-P(A\cap D)-P(B\cap C)- \displaystyle P(B\cap D)-P(C\cap D)+P(A\cap B\cap C)+P(A\cap B\cap D)+P(B\cap C\cap D)-P(A\cap B\cap C\cap D)
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