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Ex 13.3, 11 - A manufacturer has 3 machine operators A, B, C - Bayes theoram

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Ex 13.3, 11 A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A? Let A : Event that item produced by operator A B : Event that item produced by operator B C : Event that item produced by operator C D : Event that item produced is defective We need to find out the Probability that item is produced by operator A if it is defective i.e. P(A|D) So, P(A|D) = 𝑃 𝐴﷯ . 𝑃(𝐷|𝐴)﷮𝑃 𝐴﷯ . 𝑃 𝐷|𝐴﷯ + 𝑃 𝐵﷯ . 𝑃 𝐷|𝐵﷯ + 𝑃 𝐶﷯ . 𝑃 𝐷|𝐶﷯﷯ Putting Values in the formula P(A|D) = 𝑃 𝐴﷯. 𝑃(𝐷|𝐴)﷮𝑃 𝐴﷯. 𝑃 𝐷|𝐴﷯ +𝑃 𝐵﷯. 𝑃 𝐷|𝐵﷯+𝑃 𝐶﷯. 𝑃(𝐷|𝐶)﷯ = 0.5 × 0.01﷮0.5 × 0.01 + 0.3 × 0.05 + 0.2 × 0.07﷯ = 0.005﷮0.005 + 0.015 + 0.014﷯ = 0.005﷮0.034﷯ = 𝟓﷮𝟑𝟒﷯ Therefore, required probability = 5﷮34﷯

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