NCERT Class 12 · Ch 13 Exercise 13.3 · Q11
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 11
Operators A,B,C are used 50%,30%,20% of the time; their defect rates are 1%,5%,7%. Given a defective item, find P(A).
💡 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: operator A: 5/34
- Use the mutually exclusive source events with prior probabilities operator A=1/2, operator B=3/10, operator C=1/5.
- The observation likelihoods in the same order are 1/100, 1/20, 7/100. Multiply each prior by its likelihood to get joint probabilities 1/200, 3/200, 7/500.
- Total probability of the observation is 1/200 + 3/200 + 7/500 = 17/500.
- Bayes: P(operator A | observation) = 1/200 / 17/500 = 5/34.
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