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Math Help - Partitions/venn diagram

  1. #1
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    Exclamation Partitions/venn diagram

    This is the problem i was given and i cant seem to figure out how to set up the venn diagram, it's driving me crazy!:

    A car insurance company is looking at the relationship between gender and if the person has had an automobile accident. The data shows that 55% of the population is male, 67% of the population is either female or has been in an accident, and 60% of the population has never been in an accident.


    thanks so much!
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  2. #2
    MHF Contributor
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    You have male + female = 100%, and the proportion of people who have been in an accident = 40%, overlapping both male and female, which are mutually exclusive areas. 55% male gives us 45% female. 67% of the population belongs in the union of the female and accident areas, but we know that 45% is female, so 22% of the population is not female but has been in an accident, hence 22% of the population is male and has been in an accident, and 18% is female and has been in an accident. That gives us 37% is male and has not been in an accident and 27% is female and has not been in an accident.
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  3. #3
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    Smile

    OOOOh gotcha, but wouldnt it be 33% male and no accident? not 37%


    well either way, you helped a lot! thank you sooo much!
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  4. #4
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    Hello, kmagnew!

    Somehow, Venn diagrams with gender are always confusing.


    A car insurance company is looking at the relationship between gender
    and if the person has had an automobile accident.
    The data shows that 55% of the population is male,
    67% of the population is either female or has been in an accident,
    and 60% of the population has never been in an accident.
    Here's my baby-talk approach . . . I made a chart.

    \text{55 percent are male} \quad\Rightarrow\quad \text{45 percent are female}

    \text{60 percent had no accidents}\quad\Rightarrow\quad \text{40 percent had accicents}

    Write those in the chart . . .

    \begin{array}{c||c|c||c}<br />
& \text{Acc} & \text{No Acc} &  \\ \hline \hline<br />
\text{Male} & & & 55 \\ \hline<br />
\text{Female} & & & 45\\ \hline \hline<br />
& 40 & 60 \end{array}


    We need one more entry to complete the chart.

    "67% is female or has had an accident."
    . . P(\text{female }\vee\text{ accident}) \:=\:67\text{ percent}

    The opposite is: . P(\sim[\text{female }\vee\text{ accident}]) \:=\:33\text{ percent}

    By DeMorgan's Law, we have: . P(\sim\text{female } \wedge \sim\text{accident}) \;=\; 33\text{ percent}

    . . That is: . P(\text{male }\wedge\text{no accident}) \;=\;33\text{ percent}


    Enter that into the chart . . .

    \begin{array}{c||c|c||c}<br />
& \text{Acc} & \text{No Acc} &  \\ \hline \hline<br />
\text{Male} & & {\color{blue}33} & 55 \\ \hline<br />
\text{Female} & & & 45\\ \hline \hline<br />
& 40 & 60 \end{array}


    Now you can complete the chart
    . . and construct the Venn diagram.



    Use one circle for "Male" and another for "Accident".

    It should look like this:
    Code:
    
          * - - - - - - - - - - - - - - - - - - - *
          |                                       |
          |       * - - - - - - - *               |
          |       | Male          |               |
          |       |       * - - - + - - - *       |
          |       |  33%  |       |       |       |
          |       |       |  22%  |       |       |
          |       |       |       |  18%  |       |
          |       * - - - + - - - *       |       |
          |               |      Accident |       |
          |   27%         * - - - - - - - *       |
          |                                       |
          * - - - - - - - - - - - - - - - - - - - *
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  5. #5
    MHF Contributor
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    Somehow I managed to screw that one up. Sorry about that.
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  6. #6
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    thanks guys!!! that was so helpful!!!
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