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A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that  neighborhood are sick with the flu, denoted by F, while 10% are sick with the measles, denoted by M. A well known symptom of measles is a rash, denoted by R. The probability of having a rash for a child sick with the measles is 0.95. However, occasionally children with the flu also develop a rash, with conditional probability  0.08. Upon examination the child, the doctor finds a  rash. Then what is the probability that the child has the measles?

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a
91165
b
90163
c
82161
d
95167

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detailed solution

Correct option is D

A: Doctor finds a rashB1: Child has measlesS: Sick childrenP(S/F)=0.9B2: Child has flu  ⇒PB2=9/10P(S/M)=0.10PA/B1=0.95P(R/M)=0.95PA/B2=0.08P(R/F)=0.08PB1/A=0.1×0.950.1×0.95+0.9×0.08=0.0950.095+0.072=0.0950.167=95167


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