Question

The authors of a paper presented detailed case studies to medical students and to faculty at medical schools. Each participant was asked to provide a diagnosis in the case and also to indicate whether his or her confidence in the correctness of the diagnosis was high or low. Define the events C, I, and H as follows. C

C-event that diagnosis is correct
I - event that diagnosis is incorrect
H- event that confidence in the correctness of the diagnosis is high

(a) Data appearing in the paper were used to estimate the following probabilities for medical students.
P(C) = 0.262
P(HIC) = 0.344
P(I) = 0.738
P(H|I) = 0.074

Use Bayes' rule to compute the probability of a correct diagnosis given that the student's confidence level in the correctness of the diagnosis is high (Round your answer to three decimal places.)

Answer 1

0.623

Explanation:

We have to find the probability that a diagnosis is correct given that confidence in the correctness of diagnosis is high i.e.P(C/H)=?

Using Bayes' theorem the probability can be computed as

`P(C/H)=(P(C)P(H/C))/(P(C)P(H/C)+P(I)P(H/I))`

We are given that

P(C) = 0.262 , P(H/C) = 0.344 , P(I) = 0.738 and P(H/I) = 0.074.

So,

`P(C/H)=(0.262(0.344))/(0.262(0.344)+0.738(0.074))`

`P(C/H)=(0.0901)/(0.0901+0.0546)`

`P(C/H)=(0.0901)/(0.1447)`

`P(C/H)=0.6227`

P(C/H)=0.623 (rounded to three decimal places).

Thus, the probability that a diagnosis is correct given that confidence in the correctness of diagnosis is high is 0.623.