Multiple Bayesian probability

[island-boy]

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.

 

[lippyka]

Using the Bayesian formula above, we can calculate the probability that Tim has the disease as follows:P(Disease | 9 tests results negative and 1 test results positive) = P(9 tests results negative and 1 test results positive|Disease) * P(Disease) / summation of (P(9 tests results negative and 1 test results positive | No Disease) * P(No Disease)) = (0.02 * 0.05) / ((0.02*0.05) + (0.1*0.95))= 0.167 Therefore, the probability that Tim has the disease is 16.7%.