Bayes theorem

Chapter 13 Class 12 Probability (Term 2)
Concept wise

### 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?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=π.ππ π·(π"|A") = Probability of a defective bolt from machine A = 5%=5/100=π.ππ "P(B)" = Probability that the bolt is made by machine B = 35%=35/100=0.35 π·(π"|B") = Probability of a defective bolt from machine B = 4%=4/100=π.ππ "P(C)" = Probability that the bolt is made by machine C = 40%=40/100=0.40 π·(π"|C") = Probability of a defective bolt from machine C = 2%=2/100=π.ππ Putting Values in formula, "P(B|D) = " (0.35 Γ 0.04)/(0.25 Γ 0.05 + 0.35 Γ 0.04 + 0.40 Γ 0.02) = 0.014/( 0.0125 + 0.014 + 0.008 ) = 0.014/( 0.0345 ) = 140/( 345 ) = 28/69 Therefore, required probability is ππ/ππ