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NCERT Class 12 · Ch 13 Exercise 13.3 · Q3

NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 3

60% of students are hostel residents,40% day scholars. A-grade rates are 30%,20% respectively. Given an A grade, find P(hostel).
Exercise 13.3 Q3: priors, likelihoods and joints
Exercise 13.3 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: hostel: 9/13
  1. Use the mutually exclusive source events with prior probabilities hostel=3/5, day scholar=2/5.
  2. The observation likelihoods in the same order are 3/10, 1/5. Multiply each prior by its likelihood to get joint probabilities 9/50, 2/25.
  3. Total probability of the observation is 9/50 + 2/25 = 13/50.
  4. Bayes: P(hostel | observation) = 9/50 / 13/50 = 9/13.

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