Question

The probabilities associated with the expected principal source of payment for hospital discharges in the United States in the year 1990 are listed below: Principle source of Payment Probability Private Insurance 0.412 Medicare 0.325 Medicaid 0.107 Other Govt. Program ???? Self-payment 0.039 Other/ No charge 0.033 Not stated 0.025 a. (Appears as Question #23 in Blackboard) What is the probability that the principal source of payment is Other Govt. Program? b. (Appears as Question #24 in Blackboard) What is the probability that the patient’s principal source of payment is Medicare, Medicaid, or some other government program? 5 c. (Appears as Question #25 in Blackboard) Given that the principal source of payment is NOT a government program, what is the probability that it is Private Insurance?

Answer 1

a. The required probability

1-(0.412+0.325+0.107+0.039+0.033+0.025)=1-0.941=0.059

b) probability that the patient’s principal source of payment is Medicare, Medicaid, or some other government program:0.325+0.107+0.059=0.491

The payment mode can be any one of the 3,that is events are mutually exclusive of one other, so P(Medicare or Medicaid or Other Govt. Program) =P(Medicare) +P(Medicaid) +P(Other Govt Program)

c) Given that the principal source of payment is NOT a government program, the probability that it is Private Insurance=P(Private Insurance|NOT Govt Program=P(Private insurance and NOT Govt program) /P(Not Govt Program)

=P(Private insurance) /P(NOT Govt Programe) =0.412/0.941=0.4378

A private insurance mode of payment and a not Govt program can together happen iff it is only a private insurance payment