2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Probability

JEE Main & Advanced Mathematics Probability Question Bank Mock Test - Probability

  • question_answer
    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?

    A) 91/165

    B) 90/163

    C) 82/161 

    D) 95/167

    Correct Answer: D

    Solution :

    [d] A: Doctor finds a rash \[{{B}_{1}}:\]Child has measles S: Sick children \[P(S/F)=0.9\] \[{{B}_{2}}:\]Child has flu\[\Rightarrow P({{B}_{2}})=9/10\] \[P(S/M)=0.10\] \[P(A/{{B}_{1}})=0.95\] \[P(R/M)=0.95\] \[P(A/{{B}_{2}})=0.08\] \[P(R/F)=0.08\] \[P({{B}_{1}}/A)=\frac{0.1\times 0.95}{0.1\times 0.95+0.9\times 0.08}\] \[=\frac{0.095}{0.095+0.072}=\frac{0.095}{0.167}=\frac{95}{167}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner