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

Example 19 - Chapter 13 Class 12 Probability - Part 2
Example 19 - Chapter 13 Class 12 Probability - Part 3

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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?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?"P(A)" = Probability that the bolt is made by machine A = 25%=25/100=𝟎.𝟐𝟓 𝑷(𝐃"|A") = Probability of a defective bolt from machine A = 5%=5/100=𝟎.𝟎𝟓 "P(B)" = Probability that the bolt is made by machine B = 35%=35/100=0.35 𝑷(𝐃"|B") = Probability of a defective bolt from machine B = 4%=4/100=𝟎.𝟎𝟒 "P(C)" = Probability that the bolt is made by machine C = 40%=40/100=0.40 𝑷(𝐃"|C") = Probability of a defective bolt from machine C = 2%=2/100=𝟎.𝟎𝟐 Putting Values in formula, "P(B|D) = " (0.35 × 0.04)/(0.25 × 0.05 + 0.35 × 0.04 + 0.40 × 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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.