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A doctor is called to see a sick child. The doctor has prior information that 90% of sick children
in that neighborhood have the flu, while the other 10% are sick with 1 measles. Let F stand for
an event of a child being sick with flu and M stand for an event of a child being sick with
measles. Assume for simplicity that F M = , i.e., that there no other maladies in that
neighborhood. A well-known symptom of measles is a rash (the event of having which we
denote R). Assume that the probability of having a rash if one has measles is P(R|M) = 0.95.
However, occasionally children with flu also develop rash, and the probability of having a rash if
one has flu is P(R|F) = 0.08. Upon examining the child, the doctor finds a rash. What is the
probability that the child has measles?

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  • 1. A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the flu, while the other 10% are sick with 1 measles. Let F stand for an event of a child being sick with flu and M stand for an event of a child being sick with measles. Assume for simplicity that F M = , i.e., that there no other maladies in that neighborhood. A well-known symptom of measles is a rash (the event of having which we denote R). Assume that the probability of having a rash if one has measles is P(R|M) = 0.95. However, occasionally children with flu also develop rash, and the probability of having a rash if one has flu is P(R|F) = 0.08. Upon examining the child, the doctor finds a rash. What is the probability that the child has measles?