Question

in a Bolt factory machines A B and C manufacturing 25% 35% and 35% of the total of the output 5% 4% and 2% are defective balls A ball is drawn at random from the product and found to be defective what are the probabilities that it was manufactured by machine b​

Answer 1

Answer:

Let E be the probability of drawing defective bolt. Let E1, E2 and E3 be the event of drawing a bolt produced by the Machines A, B and C respectively. Then  

P(E1) = 25/100, P(E2) = 35/100, P(E3) = 40/100, P(E/E1) = 5/100, P(E/E2) = 4/100, P(E/E3) = 2/100.  

Therefore, P(E2/E) = [P(E2).P(E/E2)]/[P(E1).P(E/E1) + P(E2).P(E/E2) + P(E3).P(E/E3)]  

= [(35/100)(4/100)]/[(25/100)(5/100) + (35/100)(4/100)  

+ (40/100)(2/100)]  

= [35×4]/[25×5 + 35×4 + 40×2]  

= 140/(125 + 140 + 80)  

= 140/345  

= 28/69.