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Math Help - Probability problem

  1. #1
    Senior Member
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    Probability problem

    The question:

    Employment data at a large company reveals that 72% of the workers are married, that 44% are university graduates and that half of the university graduates are married. What is the probability that a randomly chosen worker...

    a) is neither married nor a university graduate?
    b) is married but not a university graduate?
    c) is married or is a university graduate?

    My attempt:
    I tried to convert the wording into math as follows,

    Let M = "people married"
    Let G = "people graduated"

    P(M) = 0.72
    P(G) = 0.44
    P(M \cap G) = P(G)/2 = 0.22

    a) We want to find P(M^c \cap G^c), so:

    P(M^c) = 1 - P(M) = 0.28
    P(G^c) = 1 - P(G) = 0.56

    Thus we get 0.28 x 0.56 = 0.1568

    However, this is incorrect. I'm sure I've made a wrong assumption somewhere. I'm yet to attempt part b) and c) since I'm not sure where I've gone wrong with a). Any assistance would be great.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Glitch View Post
    The question:

    Employment data at a large company reveals that 72% of the workers are married, that 44% are university graduates and that half of the university graduates are married. What is the probability that a randomly chosen worker...

    a) is neither married nor a university graduate?
    b) is married but not a university graduate?
    c) is married or is a university graduate?

    My attempt:
    I tried to convert the wording into math as follows,

    Let M = "people married"
    Let G = "people graduated"

    P(M) = 0.72
    P(G) = 0.44
    P(M \cap G) = P(G)/2 = 0.22

    a) We want to find P(M^c \cap G^c), so:

    P(M^c) = 1 - P(M) = 0.28
    P(G^c) = 1 - P(G) = 0.56

    Thus we get 0.28 x 0.56 = 0.1568

    However, this is incorrect. I'm sure I've made a wrong assumption somewhere. I'm yet to attempt part b) and c) since I'm not sure where I've gone wrong with a). Any assistance would be great.
    Have you drawn a Venn Diagram?
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  3. #3
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    No I haven't. Probably a good idea. Will report back.
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  4. #4
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    Lexington, MA (USA)
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    Hello, Glitch!

    Employment data at a large company reveals that 72% of the workers are married,
    44% are university graduates, and half of the university graduates are married.

    What is the probability that a randomly chosen worker:

    a) is neither married nor a university graduate?
    b) is married but not a university graduate?
    c) is married or is a university graduate?

    Did you consider entering all this data into a chart?

    . . \begin{array}{c||c|c||c|}<br />
& \text{Grad} & \text{non-G} & \text{Total} \\ \hline \hline<br />
\text{Married} & 22\% & 50\% & 72\% \\ \hline<br />
\text{Single} & 22\% & 6\% & 28\% \\ \hline \hline<br />
\text{Total} & 44\% & 56\% & 100\% \\ \hline \end{array}

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  5. #5
    Senior Member
    Joined
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    Thanks guys. I used a Venn diagram and worked it out. Cheers.
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