 Hello and how are you all today? The question says in a factory which manufactures nuts, machine A, B and C, manufactures respectively 25%, 35% and 40% of nuts. Of their output, 5, 4 and 2% respectively are defective nuts. A nut is drawn at random from the product and is found to be defective. We need to find the probability that it is manufactured by machine B. So this is a question which involves Bayes theorem. We are given first of all four events, event 1, event 2, event 3 and let be event A. Event E1 describes that the nut are manufactured by machine A. Similarly event 2 represents that the nuts are manufactured by machine B and event 3 says the nuts are manufactured by machine C. Whereas event A says that the nuts are defective. Now further we are given probability of selecting event 1 that is the nuts are manufactured, machine is 25% so it is 25 by 100. Probability of E2 is given to us as 35% and probability of E3 is 40%. Further we are also given that probability that a defective nut is from machine A is 5%. Probability that a defective nut is from machine B is given to us as 4% and probability that a defective nut is from machine C is 2%. So by applying Bayes theorem we will find out that the defective nut was from the machine B. So it is probability of event 2 occurring that we have picked out this defective nut from plant B. So it is equal to P E2 into P A upon E2 divided by P E1 into P A upon E1 plus P E2 into P A upon E2 plus P E3 into P A upon E3. Now we just need to substitute these values as we have found out these values above here. So we have it as 35 upon 100 into 4 upon 10 sorry 100 upon 25 upon 100 into 5 upon 100 plus 35 upon 100 into 4 upon 100 plus 40 upon 100 into 2 upon 100. On simplifying it we have 140 upon 125 plus 140 plus 80 which gives us 140 upon 345 which is further equal to 28 upon 69 and this is the answer to the session. So hope you understood it well and enjoyed it too. Have a nice day.