4. A large company offers its employees two different health insurance plans and
ID: 3045411 • Letter: 4
Question
4. A large company offers its employees two different health insurance plans and two different dental insurance plans. Plan 1 of each type is relatively inexpensive, but restricts the choice of providers, whereas plan 2 is more expensive but more flexible. The accompanying table gives the percentages of employees who have chosen the various plans [30 points Dental Plan Health Plan12 14% 27% 24% Suppose that an employee is randomly selected and both the health plan and dental plan chosen by the selected employee are determined. a. What is the probability that the selected employee has chosen more restrictive plans of each type? b. What is the probability that the selected employee has chosen at least one of the restrictive plans? If an employee has chosen expensive health plan, what is the probability that the employee select expensive dental plan too? c.Explanation / Answer
a.
Probability that the selected employee has chosen more restrictive plans = Probability that the selected employee has chosen Plan 1 of both health and dental plan = 27% = 0.27
b.
Probability that the selected employee has chosen atleast one of restrictive plans = Probability that the selected employee has chosen Plan 1 of either health or dental plan = 27% + 14% + 24% = 65% = 0.65
c.
Given that employee has chosen expensive health plans, probability that the selected employee has chosen expensive dental plans = Percentage of selected employee has chosen expensive dental and health plans / Percentage of selected employee has chosen expensive health plans
= 35% / (24% + 35%) = 0.5932
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