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Math Help - posterior probability

  1. #1
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    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?

    thanks in advance.
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  2. #2
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    Quote Originally Posted by sanv View Post
    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?

    thanks in advance.
    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 ....
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  3. #3
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    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.
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  4. #4
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    Quote Originally Posted by sanv View Post
    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%.
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