Question

"Killing Season” is a British medical term used to describe the period in August when newly qualified doctors enter the National Health Service. Around this time there is an up tick in medical misdiagnosis and surgical complications. A similar phenomenon exists in the US and occurs in the month of July. The probability that a doctor correctly diagnoses a particular illness is 0.7. Given that the doctor makes an incorrect diagnosis, the probability that the patient files a lawsuit is 0.4. At any given time 15% of all doctors are facing lawsuits.

(a) What is the probability that a doctor facing a lawsuit made a correct diagnosis.

(b) What is the probability that a doctor facing a lawsuit made an incorrect diagnosis

Answer 1

Ans:

P(facing lawsuit)=0.15

P(correctly diagnoses)=0.7

P(incorrect diagnoses)=1-0.7=0.3

P(facing lawsuit/incorrect diagnosis)=0.4

a)

P(facing lawsuit)=P(facing lawsuit and correct diagnoses)+P(facing lawsuit and incorrect diagnoses)

0.15=P(facing lawsuit and correct diagnoses)+0.4*0.3

P(facing lawsuit and correct diagnoses)=0.15-0.12=0.03

P(correct diagnoses/facing lawsuit)=P(facing lawsuit and correct diagnosis)/P(facing lawsuit)

=0.03/0.15

= 0.2

b)

P(incorrect diagnoses/facing lawsuit)=P(facing lawsuit/incorrect diagnosis)*P(incorrect diagnoses)/P(facing lawsuit)

=0.4*0.3/0.15

=0.8