

Bayes theorem
Ex 13.3, 2 Important
Ex 13.3, 3
Misc 3
Ex 13.3, 4 Important
Ex 13.3, 9
Ex 13.3, 5
Ex 13.3, 13 (MCQ) Important
Example 21 Important
Ex 13.3, 6 Important
Ex 13.3, 10 Important
Example 18 Important
Example 17 Important
Ex 13.3, 7
Ex 13.3, 8 Important
Example 19 Important You are here
Ex 13.3, 11
Ex 13.3, 12 Important
Example 37 Important
Example 20 Important
Example 33 Important
Misc 12
Misc 16 Important
Misc 13 Important
Bayes theorem
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.ππ π·(π"|A") = Probability of a defective bolt from machine A = 5%=5/100=π.ππ "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.ππ "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.ππ 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 ππ/ππ