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December 11th, 2012, 02:44 PM   #1
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Venn diagram problem

An employee benefits consulting firm has just completed a survey of the health plans offered by employers in a particular state. Among the findings are the following: 40% of employers offer no health insurance to their employees at all; 10% offer only an HMO; 20% offer only a traditional reimbursement plan; 25% offer a point-of-service (POS) plan; 10% offer both an HMO and a traditional reimbursement plan; 10% offer both a POS plan and a traditional plan; and 5% offer all three types of plans. Moreover, of employers who offer an HMO to their employees, 60% offer another type of plan as well.

a.) What fraction of employers offer only a POS plan?
b.) What fraction of employers with a traditional reimbursement plan also offer a POS plan?
c.) What fraction of employers with a POS plan offer some other type of plan as well?
d.) What fraction of employers offer their employees a choice of health plans?

Now, I don't really need help with a through d per se, but I need help in filling in the Venn diagram. Once you see it, you realize that the HMO and POS plan circle is not accounted for (which we'll call x), and the POS only plan is not accounted for. How do we figure out the values of those two areas?
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