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NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q3

NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 3

5% of men and 0.25% of women have grey hair, with equal numbers of men and women. Given a grey-haired person, find P(male).
Exercise miscellaneous Q3: priors, likelihoods and joints
Exercise miscellaneous Q3: 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: male: 20/21
  1. Use the mutually exclusive source events with prior probabilities male=1/2, female=1/2.
  2. The observation likelihoods in the same order are 1/20, 1/400. Multiply each prior by its likelihood to get joint probabilities 1/40, 1/800.
  3. Total probability of the observation is 1/40 + 1/800 = 21/800.
  4. Bayes: P(male | observation) = 1/40 / 21/800 = 20/21.

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