NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 6

Question

Choose equally from four marble boxes. Counts (red,white,black): A(1,6,3), B(6,2,2), C(8,1,1), D(0,6,4). Given a red marble, find P(A),P(B),P(C).

Accepted Answer

Final Answer: box A: 1/15; box B: 2/5; box C: 8/15 Step 1: Use the mutually exclusive source events with prior probabilities box A=1/4, box B=1/4, box C=1/4, box D=1/4. Step 2: The observation likelihoods in the same order are 1/10, 3/5, 4/5, 0. Multiply each prior by its likelihood to get joint probabilities 1/40, 3/20, 1/5, 0. Step 3: Total probability of the observation is 1/40 + 3/20 + 1/5 + 0 = 3/8. Step 4: Bayes: P(box A | observation) = 1/40 / 3/8 = 1/15. Step 5: Bayes: P(box B | observation) = 3/20 / 3/8 = 2/5. Step 6: Bayes: P(box C | observation) = 1/5 / 3/8 = 8/15.

NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 6

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