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Math Help - Venn Diagrams

  1. #1
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    Venn Diagrams

    Hi can someone please help me with this question I am very stuck

    Q) Create a venn diagram using this information: P(A)=0.4, P(B)=0.2, P(AnC)=0.04, P(BuC)=0.44, B & C are independent and A & B are mutually exclusive.

    if possible could someone please draw the venn diagram with an explanation

    the main trouble im having is where to use the fact that B & C are independent.

    thanks
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  2. #2
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    P(B\cap C) = P(B)P(C)=.2P(C) (by indeoendence)

    By the Addition Principle:

    P(B\cup C) = P(B)+P(C)-P(B\cap C)

    .44= .2+P(C)-.2P(C)

    .44= .2+.8P(C)

    .24= .8P(C)

    P(C)=.3
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  3. #3
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    Hello, wahhdoe!

    \text{Create a Venn diagram using this information:}

    . . P(A)=0.4,\;P(B)=0.2,\;P(A \cap C)=0.04,\;P(B \cup C)=0.44

    . . B\text{ and }C\text{ are independent, and }A\text{ and }B\text{ are mutually exclusive.}

    DrSteve did an excellent job!

    He found that: . P(C) = 0.3

    Since \,B and \,C are independent:
    . . P(B \cap C) \:=\: P(B)\cdot P(C) \:=\:(0.2)(0.3) \:=\:0.06


    The Venn diagram looks like this:

    Code:
    
          *-----------------------------------------------*
          |                                               |
          |   *---------------*       *---------------*   |
          |   | A             |       |             B |   |
          |   |   0.36        |       |        0.14   |   |
          |   |               |       |               |   |
          |   |       *-------+-------+-------*       |   |
          |   |       |  0.04 |       |  0.06 |       |   |
          |   |       |       |       |       |       |   |
          |   *-------+-------*       *-------+-------*   |
          |           |          0.2          |           |
          |           |           C           |           |
          |   0.2     *-----------------------*           |
          |                                               |
          *-----------------------------------------------*
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