Example 19 - Chapter 13 Class 12 Probability (Term 2)

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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