1. ## posterior probability

Hi,

I have the following question where I have to calculate the posterior probabilty of a person having a certain disease.

P(patient has disease|heterosexual, non drug user) = 0.00001
P(Test pos. | disease) = 0.9
P(Test pos. | no disease) = 0.2

to write it in an easier way:

P(D) = 0.0001
P(pos|D) = 0.9
P(pos|no D) = 0.2

P(no D) = 1 - P(D) ???

I used bayes theorem as follows:

posterior = (P(pos|D) * P(D))/(P(pos|D)*P(D) + P(pos|no D) * P(no D))

and i get as a result: 0.0045%.

Did I interpret the question right?

2. Originally Posted by sanv
Hi,

I have the following question where I have to calculate the posterior probabilty of a person having a certain disease.

P(patient has disease|heterosexual, non drug user) = 0.00001
P(Test pos. | disease) = 0.9
P(Test pos. | no disease) = 0.2

to write it in an easier way:

P(D) = 0.0001
P(pos|D) = 0.9
P(pos|no D) = 0.2

P(no D) = 1 - P(D) ???

I used bayes theorem as follows:

posterior = (P(pos|D) * P(D))/(P(pos|D)*P(D) + P(pos|no D) * P(no D))

and i get as a result: 0.0045%.

Did I interpret the question right?

Are you trying to calculate Pr(heterosexual, non drug user has the disease | Test pos) ?

In which case, we have a particular type of person. Otherwise, more information is required if it's just a random type of person ....

3. I was only given those facts and the question was "calculate the posterior probabilty of a person having disease". That's all I was given, so I interpreted the question with the facts given as shown before.

4. Originally Posted by sanv
I was only given those facts and the question was "calculate the posterior probabilty of a person having disease". That's all I was given, so I interpreted the question with the facts given as shown before.
If you're trying to calculate Pr(heterosexual, non drug user has the disease | Test pos), then I agree with your calculation. Except I would say either that the probablity is 0.000045 or that the chance is 0.0045%.