Doctor! Doctor!

A doctor is called to see a sick child. The doctor knows (prior to visit) that 90% of the children in that neighborhood are sick with flu while 10% are sick with conditional probability 0.08.

Upon examination of the child, doctor finds a rash. What is the probability that the child has measles?

If the answer is of the form \(\dfrac{p}{q}\) where \(p\) and \(q\) are coprime positive integers, find \(p+q\).

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