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NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q7

NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 7

In the stated model, baseline heart-attack probability is 40%. Two equally chosen options reduce risk by 30% (meditation/yoga) or 25% (drug). Given a heart attack afterward, find P(meditation/yoga).
Exercise miscellaneous Q7: priors, likelihoods and joints
Exercise miscellaneous Q7: 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: meditation/yoga: 14/29
  1. Use the mutually exclusive source events with prior probabilities meditation/yoga=1/2, drug=1/2.
  2. The observation likelihoods in the same order are 7/25, 3/10. Multiply each prior by its likelihood to get joint probabilities 7/50, 3/20.
  3. Total probability of the observation is 7/50 + 3/20 = 29/100.
  4. Bayes: P(meditation/yoga | observation) = 7/50 / 29/100 = 14/29.

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