A doctor does a video call with a sick child. He knows that 95%
of children sick in this area have the flu, while 5% have measles.
Assume for simplicity that these are the only options.
Children with measles often have a rash. Suppose that the
probability of a child having a rash if he has measles is 94%, that
is P ( R | M ) = .94. However, a child with the flu could also have
a rash. Suppose that roughly 8% of children with the flu have a
rash. We can infer then, that P ( R | F ) = .08.
Upon examining the child, the doctor finds that the child has a
rash. What is the probability that the child has measles?