Results 1 to 4 of 4

Math Help - A probability question

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    New Zealand
    Posts
    8

    A probability question

    I am trying to revise for a test, and am working through some prep questions. I am struggling on this one, could anyone help?

    Suppose there is a medical diagnostic test for a disease. The sensitivity of the
    test is .95. This means that if a person has the disease, the probability that the
    test gives a positive response is .95. The specificity of the test is .90. This
    means that if a person does not have the disease, the probability that the test
    gives a negative response is .90, or that the false positive rate of the test is .10.
    In the population, 1% of the people have the disease.
    What is the probability that a person tested has the disease, given the results of the test is positive? Let
    D be the event "the person has the disease" and let T be the event "the test
    gives a positive result."

    Any help would be much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: A probability question

    n = normal
    s = sick
    + = test positive
    - = test negative

    Pr(n+) = .1 * .99 = .099
    Pr(n-) = .90 * .99 = .891
    Pr(s+) = .95 * .01 = .0095
    Pr(s-) = .05 * .01 = .0005

    Pr(s|+) = .0095/(.099+.0095) = .08756 (=8.756%)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1

    Re: A probability question

    Quote Originally Posted by bryce09 View Post
    Suppose there is a medical diagnostic test for a disease. The sensitivity of the
    test is .95. This means that if a person has the disease, the probability that the
    test gives a positive response is .95. The specificity of the test is .90. This
    means that if a person does not have the disease, the probability that the test
    gives a negative response is .90, or that the false positive rate of the test is .10.
    In the population, 1% of the people have the disease.
    What is the probability that a person tested has the disease, given the results of the test is positive? Let
    D be the event "the person has the disease" and let T be the event "the test
    gives a positive result."
    I think that I answered this elsewhere. Let D means a person has the disease and D^c means a person does not have the disease. You are given: P(+|D)=0.95,~P(-|D^c)=0.90,~\&~P(D)=0.01.
    From that we conclude P(-|D)=0.05,~P(+|D^c)=0.10,~\&~P(D^c)=0.99~.
    Now P(+)=P(+|D)P(D)+P(+|D^c)P(D^c)

    The question is P(D|+)=\frac{P(D\cap +)}{P(+)}~.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2012
    From
    New Zealand
    Posts
    8

    Re: A probability question

    Thanks for those answers, both were really helpful
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: February 10th 2013, 02:11 PM
  2. Probability question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 18th 2012, 09:52 AM
  3. Probability question involving (A given B type question )
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 9th 2009, 09:08 AM
  4. Probability Question
    Posted in the Statistics Forum
    Replies: 6
    Last Post: October 17th 2009, 07:36 AM
  5. A probability question and an Expectations question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 29th 2006, 06:13 PM

Search Tags


/mathhelpforum @mathhelpforum