A large company offers its employees two different health insurance plans and tw

Question

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 choices of health providers, whereas plan 2 is more expensive but more flexible. The accompanying table gives the percentages of employees who have chosen their health and dental insurance plans: Suppose that an employee is randomly selected and both the health plan and dental plan chosen by the selected employee are determined. What are the four possible outcomes (called also simple events)? What is the probability that the selected employee has chosen the more restrictive plan of each type? What is the probability that the selected employee has chosen the more flexible dental plan? If a randomly selected employee has chosen the more flexible dental plan, what is the conditional probability that the selected employee has also chosen the more flexible health plan?

Explanation / Answer

(a)

Let H shows the health plan and D shows the dental plan. So possible sample space is

S = {H1D1, H1D2, H2D1, H2D2}

(b)

Since plan 1 are more restricted so the probability that the selected employee has chosen the more restrictive plan of each type is

P(H1D1) = 0.27

(c)

The probability that the selected employee has chosen the more flexible dental plan is

P(more flexible dental plan) = P(H1D2 or H2D2) = P(H1D2) +P(H2D2) = 0.14 +0.35 = 0.49

(d)

P(H2D2) = 0.35

So the required conditional probability is

P(H2D2 |more flexible dental plan) = P(H2D2) / P(more flexible dental plan) = 0.35 / 0.49 = 0.7143

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