1. ## 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!

2. 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.

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

well either way, you helped a lot! thank you sooo much!

4. 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.

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

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

Write those in the chart . . .

$\displaystyle \begin{array}{c||c|c||c} & \text{Acc} & \text{No Acc} & \\ \hline \hline \text{Male} & & & 55 \\ \hline \text{Female} & & & 45\\ \hline \hline & 40 & 60 \end{array}$

We need one more entry to complete the chart.

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

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

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

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

Enter that into the chart . . .

$\displaystyle \begin{array}{c||c|c||c} & \text{Acc} & \text{No Acc} & \\ \hline \hline \text{Male} & & {\color{blue}33} & 55 \\ \hline \text{Female} & & & 45\\ \hline \hline & 40 & 60 \end{array}$

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%         * - - - - - - - *       |
|                                       |
* - - - - - - - - - - - - - - - - - - - *

5. Somehow I managed to screw that one up. Sorry about that.

6. thanks guys!!! that was so helpful!!!