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Math Help - Bayes Theorem question

  1. #1
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    Bayes Theorem question

    Suppose the probability of a person having a headache is 0.01
    the probability of a person having a fever given that the person has a headache is 0.4
    the probability of a person having a fever is 0.02

    What is the probability that if a person has a headache given that the person have a fever?
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  2. #2
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    Quote Originally Posted by Frostking View Post
    Suppose the probability of a person having a headache is 0.01
    the probability of a person having a fever given that the person has a headache is 0.4
    the probability of a person having a fever is 0.02

    What is the probability that if a person has a headache given that the person have a fever?
    Let A denote a headache and B denote a fever.

    Therefore, we have:
    P(A) = 0.01

    P(B) = 0.02

    P(B|A) = 0.4

    Bayes Rule states:

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    Evaluating, we get:

    P(A \cap B) = (0.4)(0.01)

    P(A \cap B) = 0.004

    Now, use Bayes Rule again for our question that asks for a headache given a fever. That is:

    P(A|B) = \frac{P(A \cap B)}{P(B)}

    Evaluating, we get:

    P(A|B) = \frac{0.004}{0.02}

    P(A|B) = 0.2

    If you ever have a complement problem using Bayes Rule, you can use my calculator. It won't solve this particular problem, but I'll build that in the future. It solves certain other problems:

    Bayes Rule
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  3. #3
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    Bayes Theorum question

    Thank you very much for your prompt, through and very helpful reply!!!!
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