# Example 19

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

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 × 0.040.25 × 0.05 + 0.35 × 0.04 + 0.04 × 0.02 = 0.014 0.0125 + 0.014 + 0.008 = 0.014 0.0345 = 140 345 = 2869 Therefore, required probability is 𝟐𝟖𝟔𝟗

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Chapter 13 Class 12 Probability

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.