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Math Help - probability question, not sure how to write this equation out.

  1. #1
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    probability question, not sure how to write this equation out.

    Suppose that the probability of a person having a headache is 0.01, that the probability of a person having a fever given that the person has a headache is 0.4, and that the probability of a person having a fever is 0.02. Find the probability that a person has a headache given that the person has a fever.
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  2. #2
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    Re: probability question, not sure how to write this equation out.

    Here's how I would do that: Imagine 10000 people. 0.01 of them, or 100, have a headache. 0.04 of those people, or 4, have fever. But we also know that 0.02 of the original 10000, or 200, have a fever. So 4 of the 200 people with a fever also have a headache. Given that person has a fever, there is a 4/200= .02 probability they also have a headache.
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    Re: probability question, not sure how to write this equation out.

    Quote Originally Posted by madmilitia View Post
    Suppose that the probability of a person having a headache is 0.01, that the probability of a person having a fever given that the person has a headache is 0.4, and that the probability of a person having a fever is 0.02. Find the probability that a person has a headache given that the person has a fever.
    After having seen reply #2, I deleted my first. You now have the answer.

    So here are some more ideas.
    Given: \mathcal{P}(H)=.01,~\mathcal{P}(F)=.02,~\& ~\mathcal{P}(F|H)=.04.

    You want to find \mathcal{P}(H|F)=\frac{\mathcal{P}(H\cap F)}{\mathcal{P}(F)},

    So to do that, you need to know \mathcal{P}(H\cap F).
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