Example 19 - In a factory manufactures bolts, machines A, B, C - Examples

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  1. Chapter 13 Class 12 Probability
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Example 19 In a factory which manufactures bolts, machines A, B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B? Let A : bolt manufactured from machine A B : bolt manufactured from machine B C : bolt manufactured from machine C D : bolt is defective We need to find the Probability that the bolt is manufactured by machine B, if it is defective i.e. P(B|D) So, P(B|D) = 𝑃 𝐵﷯. 𝑃(𝐷|𝐵)﷮𝑃 𝐴﷯. 𝑃 𝐷|𝐴﷯ + 𝑃 𝐵﷯. 𝑃 𝐷|𝐵﷯ + 𝑃 𝐶﷯. 𝑃 𝐷|𝐶﷯﷯ Putting Values in formula, P(B|D) = 0.35 × 0.04﷮0.25 × 0.05 + 0.35 × 0.04 + 0.04 × 0.02﷯ = 0.014﷮ 0.0125 + 0.014 + 0.008 ﷯ = 0.014﷮ 0.0345 ﷯ = 140﷮ 345 ﷯ = 28﷮69﷯ Therefore, required probability is 𝟐𝟖﷮𝟔𝟗﷯

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