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NCERT Class 12 · Ch 13 Exercise 13.3 · Q9

NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 9

Groups I,II win with probabilities 0.6,0.4. New-product probabilities after winning are 0.7,0.3. Given a new product, find P(group II won).
Exercise 13.3 Q9: priors, likelihoods and joints
Exercise 13.3 Q9: 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: group II: 2/9
  1. Use the mutually exclusive source events with prior probabilities group I=3/5, group II=2/5.
  2. The observation likelihoods in the same order are 7/10, 3/10. Multiply each prior by its likelihood to get joint probabilities 21/50, 3/25.
  3. Total probability of the observation is 21/50 + 3/25 = 27/50.
  4. Bayes: P(group II | observation) = 3/25 / 27/50 = 2/9.

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