Question

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 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?

          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 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?

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 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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