Results 1 to 4 of 4

Math Help - Bayes Problem

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    2

    Bayes Problem

    Can't seem to figure this one out. Any help would be appreciated:

    A positive result on a test for diabetes is correct 90% of the time, and a negative result is correct 95% of the time. If 10% of the population has diabetes, what is the probability that a randomly selected person will have a false positive test result?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Pim
    Pim is offline
    Member
    Joined
    Dec 2008
    From
    The Netherlands
    Posts
    91
    I'm not sure you stated the problem correctly. In this form it's not a Bayesian problem.

    As it is now, you are looking for a person who belongs to the non-diabetes group (.9 probability) and then gets an incorrect positive test result. (.1 probability) You then multiply these to get your answer.

    It would be a Bayesian problem if the question was: Given a positive result, what is the chance that person has diabetes?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2010
    Posts
    185
    Thanks
    13
    Hypothesis are
    H_1:=\{person\, has \, diabetes\} \Rightarrow P(H_1)=0.1
    H_2:=\{person\, doesn't\, have \, diabetes\} \Rightarrow P(H_1)=0.9

    Define events
    A=\{test\, is \, positive\} and B=\{test\, is \, negative\}.

    Then
    P(A|H_1)=0.9
    P(A|H_2)=0.1
    P(B|H_1)=0.05
    P(B|H_2)=0.95

    You have to find the probability that person has a false positive result hence you have to find P(A\cap H_2)=P(A|H_2)P(H_2)=0.1 \cdot 0.9=0.09=9\%
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2010
    Posts
    2
    Thank you both. I found the wording of the problem somewhat confusing.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Bayes' Theorem problem.
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 12th 2011, 08:25 PM
  2. bayes act problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 29th 2010, 11:04 AM
  3. Bayes Problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 4th 2010, 07:21 PM
  4. bayes - naive bayes and bayesian networks
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 8th 2008, 02:40 PM
  5. Bayes theorem problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 30th 2007, 04:56 AM

Search Tags


/mathhelpforum @mathhelpforum