Expert: Josh - 6/10/2009

Question
In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work are in car pools.If 40 percent employees of Company X are in car pools, what percent of employees of Company X live ten miles or less from work and are in car pools?

Answer
Hello Shruti,

I had a quick look at the question, I think it goes like this.

Let M denote the set of employees who live over ten miles from work.
Let C denote the set of employees who participate in car pools.

Of course, these two sets are NOT exclusive. For instance, there is a group of people who are both M and C. There are also people who are not M and C (i.e., live "within" 10 miles from work and still car pool).

We were told that M represents 30% of the population. For convenience let us write |M|=0.3 for the size of M. Note: When the value is 1, the set includes the entire population (all the employees in the context of this question).

Since 60% of people who belong to set M car pool, |M and C| = 0.6*0.3 = 0.18. We were also told that 40% of all employees car pool irrespective of other factors. So, the size of set C, |C|=0.4.

Finally, as |M and C| + |not(M) and C| = |C|, we have |not(M) and C| = |C| - |M and C| = 0.4-0.18 = 0.22 (i.e., 24% relative to the whole population of employees). You can draw a Venn diagram to see this relationship clearly.