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Math Help - Simple beginners probability question

  1. #1
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    Simple beginners probability question

    Hi, could you check over my work to see if this is correct?

    You are given P(A \cup B)=0.7 and P(A \cup B\prime)=0.9. Determine P(A).

    Find B:
    P(A \cup B\prime)=1-B=0.9 \\ B=0.1

    Then:
    P(A)=P(A\cup B)-P(B)=0.7-0.1 \\ =0.6
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  2. #2
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    Quote Originally Posted by greatsheelephant View Post
    Hi, could you check over my work to see if this is correct?

    You are given P(A \cup B)=0.7 and P(A \cup B\prime)=0.9. Determine P(A).

    Find B:
    P(A \cup B\prime)=1-B=0.9 \\ B=0.1

    Then:
    P(A)=P(A\cup B)-P(B)=0.7-0.1 \\ =0.6
    P(A)=P(A\cup B)-P(B)+P(A\cap B)
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  3. #3
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    From the given we get:
     P(A) + P(B) - P(A \cap B) = 0.7~\&
    P(A) + P(B') - P(A \cap B') = 0.9.
    Add those together.
    Use these facts: P(B)+P(B')=1~\&~ P(A \cap B) + P(A \cap B')=P(A) .
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  4. #4
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    Hello, greatsheelephant!

    \text{Given: }\;P(A \cup B)\,=\,0.7,\;P(A \cup B')\,=\,0.9
    \text{Determine }P(A).

    Using DeMorgan's Laws: . \begin{Bmatrix} P(A \cup B) \:=\:0.7 & \Rightarrow & P(A' \cap B') \:=\: 0.3 \\ \\[-3mm]<br />
P(A \cup B') \:=\: 0.9 & \Rightarrow & P(A' \cap B) \:=\: 0.1 \end{Bmatrix}


    I used a Venn diagram:

    Code:
    
          *-------------------------------*
          |                               |
          |   *---------------*           |
          |   |/A/////////////|           |
          |   |///////////////|           |
          |   |///////*-------+-------*   |
          |   |///////|///////|       |   |
          |   |///////|///////|       |   |
          |   |///////|///////|  0.1  |   |
          |   *-------+-------*       |   |
          |           |             B |   |
          |   0.3     *---------------*   |
          |                               |
          *-------------------------------*

    Then it is evident that: . P(A) \,=\,0.6

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  5. #5
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    Thank you! I came to 0.6 as well but I went about it by finding B, then subtracting the remaining union from the sample space, 1.
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