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NCERT Class 12 · Ch 13 Exercise 13.3 · Q4

NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 4

A student knows an MCQ answer with probability 3/4; otherwise guesses and is correct with probability 1/4. Given a correct answer, find P(knew).
Exercise 13.3 Q4: priors, likelihoods and joints
Exercise 13.3 Q4: 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: knows: 12/13
  1. Use the mutually exclusive source events with prior probabilities knows=3/4, guesses=1/4.
  2. The observation likelihoods in the same order are 1, 1/4. Multiply each prior by its likelihood to get joint probabilities 3/4, 1/16.
  3. Total probability of the observation is 3/4 + 1/16 = 13/16.
  4. Bayes: P(knows | observation) = 3/4 / 13/16 = 12/13.

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All Questions in Probability — Exercise 13.3

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