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 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:

Suppose that an employee is randomly selected and both the health plan and dental plan
chosen by the selected employee are determined.
1
[4] a. What are the four possible outcomes (called also simple events)?
[4] b. What is the probability that the selected employee has chosen to save as much
money as possible?
[4] c. What is the probability that the employee has chosen the more flexible dental plan?

Explanation / Answer

Dental Plan

a) The possible outcomes that is sample events are given by,

S = { H1D1} ,{H1D2},{H2D1},{H2D2 }

B) Plan 1 of each type is relatively inexpensive.

Hence to save as much money as possible employee choose plan H1D1

Hence p ( H1D1) = 0.27

C) plan 2 is more expensive but more flexible The more flexible plans are H1D2 and H2D2

Hence the probability that the employee has chosen the more flexible dental plan is

p ( H1D2) + p (H2D2) = 0.14+0.35 = 0.49

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