Patient,Doctor and accuracy of diagnosis.

Probability Level pending

Suppose that a patient is being diagnosed and it is known that 1% of similar patients have the disease.Suppose also that the doctor diagnosed positive and diagnosis test is 80% accurate. What is the probability that the patient have disease given that diagnosis test is positive.

0.091 0.134 0.08 0.15 3.921E-2

1 solution

Winod Dhamnekar
Jun 23, 2019

Let D be the event that the patient has the disease and T be the event that the his diagnosis test is positive. Then we know that $P(T|D)=0.80=P(T^C|D^C)$ . Using Bayes'theorem and the law of total probability, we can compute, $P(D|T)=\frac{P(T|D)P(D)}{P(T)}$ $P(D|T)=\frac{P(T|D)P(D)}{P(T|D)P(D)+P(T|D^C)P(D^C)}$

$P(D|T)=0.039212$

If accuracy of diagnosis is only $50\%$ , Then the probability that the patient have disease given that the diagnosis test is positive,is only $1\%$

Patient,Doctor and accuracy of diagnosis.

1 solution

0 pending reports