A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighbourhood are sick with the flu, denoted by `F ,` while 10% are sick with the measles, denoted by `Mdot` A well-known symptom of measles is a rash, denoted by R. The probability 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. The what is the probability that the child has the measles? `91//165` b. `90//163` c. `82//161` d. `95//167`

Options

A. `91//165`
B. `90//163`
C. `82//161`
D. `95//167`

Answer

D

Explanation

A: Doctor finds a rash
`B_(1):` Child has measles
S: Sick children
`P(S//F)=0.9`
`B_(2):"Child has flu"impliesP(B_(2))=9//10`
`{:(P(S//M)=0.10,),(P(A//B_(1))=0.95,),(P(R//M)=0.95,),(P(A//B_(2))=0.08,),(P(R//F)=0.08,):}`
`P(B_(1)//A)=(0.1xx0.95)/(0.1xx0.95+0.9xx0.08)`
`=(0.095)/(0.095+0.072)`
`=(0.095)/(0.67)=(95)/(167)`