NCERT Class 12 · Ch 13 Exercise 13.3 · Q2
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 2
Choose equally between bags I:4 red,4 black and II:2 red,6 black. A red ball is drawn. Find P(bag I|red).
💡 Concept Hints
- Define the events and identify which event is being conditioned on.
- 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: bag I: 2/3
- Use the mutually exclusive source events with prior probabilities bag I=1/2, bag II=1/2.
- The observation likelihoods in the same order are 1/2, 1/4. Multiply each prior by its likelihood to get joint probabilities 1/4, 1/8.
- Total probability of the observation is 1/4 + 1/8 = 3/8.
- Bayes: P(bag I | observation) = 1/4 / 3/8 = 2/3.
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