Give solution of 9th question
9. In a bolt factory, machines A, B and C manufacture respectively 25%, 35% and 40 % of the total bolts. Of their output 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. What is the probability that the bolt drawn is defective?

Let A be the event that product is manufactured by machine ASo,PA=25%=0.25Let B be the event that product is manufactured by machine BSo,PB=35%=0.35Let C be the event that product is manufactured by machine ASo,PC=40%=0.40AndE be the event that product is defectiveNowProbabilty that a defective product is manufactured by machine A, PE/A=5%=0.05Probabilty that a defective product is manufactured by machine B, PE/B=4%=0.04Probabilty that a defective product is manufactured by machine C, PE/C=2%=0.02ThusBy total probability, PE=PAPE/A+PBPE/B+PCPE/CPE=0.25×0.05+0.35×0.04+0.40×0.02=0.0345

  • 1
What are you looking for?