Multiple Bayesian probability

  1. I know the Bayesian formula is given by the ff:

    P(Ei|A) = P(A | Ei) * P (Ei) / summation of P (A | En) * P (En) over n

    however how do you solve this type of problem:

    The probability of a person having a disease is 5%,
    The probability of testing negative in a checkup given that you have a disease is 2% (the test is not accurate, hence this result).
    The probability of testing positive given that you do not have the disease is 10%

    Tim takes the test 10 times, only one of which returns positve, what is the probability that Tim has the disease?

    that is what is P(disease | 9 tests results negative and 1 test results positive)?

    any hints would be great, thanks.
     
  2. jcsd
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