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

✅ Step-by-Step Solution

1. Use the mutually exclusive source events with prior probabilities lost diamond=1/4, lost non-diamond=3/4.
2. The observation likelihoods in the same order are 22/425, 26/425. Multiply each prior by its likelihood to get joint probabilities 11/850, 39/850.
3. Total probability of the observation is 11/850 + 39/850 = 1/17.
4. Bayes: P(lost diamond | observation) = 11/850 / 1/17 = 11/50.
5. Equivalently, after identifying two diamonds, the lost card is uniform among the other 50 cards, of which 11 are diamonds; the posterior is 11/50.