NCERT Class 12 · Ch 13 Exercise 13.3 · Q8
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 8
Machines A,B produce 60%,40% of output; defect rates are 2%,1%. Given a defective item, find P(B).
💡 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: machine B: 1/4
- Use the mutually exclusive source events with prior probabilities machine A=3/5, machine B=2/5.
- The observation likelihoods in the same order are 1/50, 1/100. Multiply each prior by its likelihood to get joint probabilities 3/250, 1/250.
- Total probability of the observation is 3/250 + 1/250 = 2/125.
- Bayes: P(machine B | observation) = 1/250 / 2/125 = 1/4.
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