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Thread: Probability help

  1. #1
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    Probability help




    Hey guys I'm new to this site, and I could really use some help!

    I am currently in a stats class and I'm so terrible with numbers it's not even funny. I have on hw question that seems easy enough and I've worked through it some, but I'm just not sure if it is correct.

    Here is the problem:
    The overall prevalence of HIV is 2% of the population. The HIV diagnostic exam has
    sensitivity (probability of detecting HIV given that the person is infected) of 0.98 and specificity
    (probability of giving a negative result given that the person is not infected) of 0.95. What is the
    probability that the person is infected, given a positive test result? Based on your previous answer,
    should HIV testing be required for everyone?


    And here is what I have worked out so far:
    P(positive test result / person is infected) = 0.98
    or, P(positive test result and person is infected)/P(person is infected) = 0.98
    or, P(positive test result and person is infected) = 0.98*0.02 = 0.0196

    Can someone please tell me if this is right or if not help me work through it so I can understand!

    Thanks!

  2. #2
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    Re: Probability help

    hi,
    you need to work out the probability(infected|positive) by applying the Bayes formula

    p(A|B)=P(B|A)*P(A)/P(B) with A - infected, B - test positive.

    P(B) can be expressed as P(B)=P(B|A)*P(A)+ P(B|not A)*P(not A).

    The necessary conditional probabilities are provided in the problem. Good luck and don't be too surprised

    regards
    rogojel

  3. The Following User Says Thank You to rogojel For This Useful Post:

    cthurman (01-16-2014)

  4. #3
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    Re: Probability help


    Okay so I'm missing a step! Thanks this was really helpful

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