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NCERT Class 12 · Ch 13 Exercise 13.3 · Q5

NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 5

In the stated test model, disease prevalence is 0.1%, detection is 99%, and false-positive rate among healthy people is 0.5%. Find P(disease|positive).
Exercise 13.3 Q5: priors, likelihoods and joints
Exercise 13.3 Q5: priors, likelihoods and joints

💡 Concept Hints

  1. Define the events and identify which event is being conditioned on.
  2. Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.

✅ Step-by-Step Solution

Final Answer: disease: 22/133
  1. Use the mutually exclusive source events with prior probabilities disease=1/1000, healthy=999/1000.
  2. The observation likelihoods in the same order are 99/100, 1/200. Multiply each prior by its likelihood to get joint probabilities 99/100000, 999/200000.
  3. Total probability of the observation is 99/100000 + 999/200000 = 1197/200000.
  4. Bayes: P(disease | observation) = 99/100000 / 1197/200000 = 22/133.

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