A doctor is called to see a sick child. The doctor has prior information that 95% of sick children in that neighborhood have the flu, while the other 5% 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 is the entire sample space of illness among children 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 conditional probability that the child has measles, M? First write down the answer that comes to your mind without using a calculator. Then calculate the relevant conditional probability according to Bayes’ law. What accounts for the difference in the two answers and how does it relate to the evidence on Bayes’ law in the human population?
A doctor is called to see a sick child. The doctor has prior
information that 95% of sick children in that neighborhood have the flu, while
the other 5% are sick with measles. Let F stand for an
with flu and M stand for an event of a child being sick with measles. Assume
for simplicity that F ∪ M is the entire sample space of illness among children
in that neighborhood
A well-known symptom of measles is a rash (the event of having which we
denote R). Assume that the
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 conditional
probability that the child has measles, M? First write down the answer that
comes to your mind without using a calculator. Then calculate the relevant conditional probability according to Bayes’ law. What accounts for the difference
in the two answers and how does it relate to the evidence on Bayes’ law in the
human population?
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