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NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q10

NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 10

Bag I has 3 red,4 black; bag II has 4 red,5 black. Transfer a random ball from I to II, then draw from II. Given that draw is red, find P(transferred black).
Exercise miscellaneous Q10: priors, likelihoods and joints
Exercise miscellaneous Q10: 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: transfer black: 16/31
  1. Use the mutually exclusive source events with prior probabilities transfer red=3/7, transfer black=4/7.
  2. The observation likelihoods in the same order are 1/2, 2/5. Multiply each prior by its likelihood to get joint probabilities 3/14, 8/35.
  3. Total probability of the observation is 3/14 + 8/35 = 31/70.
  4. Bayes: P(transfer black | observation) = 8/35 / 31/70 = 16/31.

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