Results 1 to 4 of 4

Math Help - Conditional probability.

  1. #1
    Senior Member
    Joined
    Jan 2010
    Posts
    273

    Conditional probability.

    Half percent of a population has a particular disease. A test is developed for the disease. The test gives a false positive 3% of the time and a false negative 2% of the time.

    (a) What is the probability that joe (a random person) tests positive?

    (b) Joe just got the bad news that the test came back positive; what is the probability that Joe has the disease?


    I'm not sure what false positive and false negative mean, does test positive imply he has the disease?
    So, the prob that joe tests positive will be 0.5%+3%?

    and part b will be 0.5%+2%?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Conditional probability.

    Quote Originally Posted by wopashui View Post
    Half percent of a population has a particular disease. A test is developed for the disease. The test gives a false positive 3% of the time and a false negative 2% of the time.

    (a) What is the probability that joe (a random person) tests positive?

    (b) Joe just got the bad news that the test came back positive; what is the probability that Joe has the disease?


    I'm not sure what false positive and false negative mean, does test positive imply he has the disease?
    So, the prob that joe tests positive will be 0.5%+3%?

    and part b will be 0.5%+2%?
    A false positive occurs when the test indicates that Joe has the disease when in fact he hasn't.

    A false negative occurs when the test indicates that Joe doers not have the disease when in fact he does.

    The test gives a false positive 3% of the time and a false negative 2% of the time.
    Pr(+ve | no disease) = 0.03.

    Pr(-ve | disease) = 0.02.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2010
    Posts
    273

    Re: Conditional probability.

    Quote Originally Posted by mr fantastic View Post
    A false positive occurs when the test indicates that Joe has the disease when in fact he hasn't.

    A false negative occurs when the test indicates that Joe doers not have the disease when in fact he does.


    Pr(+ve | no disease) = 0.03.

    Pr(-ve | disease) = 0.02.


    so for part a let A be the event of having the disease, B of not having the disease
    I got A \cap positive + B \cappositive= 0.5%x98%+99.5%x3%


    and part b, i use bayees rule {98%x0.5%}/{99.5%x3%+98%x0.5%}

    am i on the right track?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Conditional probability.

    Quote Originally Posted by wopashui View Post
    so for part a let A be the event of having the disease, B of not having the disease
    I got A \cap positive + B \cappositive= 0.5%x98%+99.5%x3%


    and part b, i use bayees rule {98%x0.5%}/{99.5%x3%+98%x0.5%}

    am i on the right track?
    Well, I'd use 0.005, 0.98, 0.995, 0.03 etc. NOT percentages.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 22nd 2011, 02:39 AM
  2. Conditional Probability using the Law of Total Probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 7th 2010, 04:01 AM
  3. Conditional probability.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 6th 2010, 07:45 PM
  4. need help with conditional probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 21st 2009, 06:34 PM
  5. Continuous probability - conditional probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 1st 2009, 02:21 AM

Search Tags


/mathhelpforum @mathhelpforum