Question

1)    A study on medical malpractice found that 23% of all doctors had been sued. Of those doctors who had been sued, 20% work for HMOs. Industry statistics show that 30% of all doctors work for HMOs.

a)   What is the probability that a doctor who had not been sued works for an HMO?

b)   What is the probability that a doctor who works for an HMO has been sued?

c)   What is the probability that a doctor who does not work for an HMO has been sued?

d)   Who will pay higher malpractice insurance, HMO or non-HMO doctors? Why?

Answer 1

Question 1

Pr(Medical malpracticed doctor sued) = 0.23

Pr(Work for HMOs l Sued) = 0.20

Pr(doctors worked for HMO) = 0.30

(a)

Here

Pr(Doctors worked for HMO) = Pr(doctor Sued) * Pr(Work for HMOs l Sued) + Pr(Doctor not sued) * Pr(Work for HMOs l Not Sued)

0.30 = 0.23 * 0.20 + (1 - 0.23) * Pr(Work for HMOs l Not Sued)

Pr(Work for HMOs l Not Sued) = [0.30 - 0.23 * 0.20]/ (1 - 0.23) = 0.33

(b) Pr(Sued l Work for HMO) = (0.23 * 0.20)/0.30 = 0.1533

(c) Pr(Sued lDoen't work for HMO) = (0.23 * 0.80)/ (1 - 0.30) = 0.263

(d) Here non HMO doctors willpay higher malpracitce insurance as they have higher percentage of sued doctors.