 Hello and how are you all today? My name is Priyanka and let us discuss this question. It says, a company has two plants to manufacture machines. Plant A manufactures 70% and plant B manufacture 30% machines. At plant A, 80% of the machines are rated of standard quality and plant B 90% of the machines are rated of standard quality. A machine is chosen at random and is found to be standard quality. What is the probability that it was manufactured by plant A? So let us discuss this question together here. Let E be the event that the machine is of standard quality. Let B1 be the event that the machine is manufactured by plant A and let B2 be the event that the machine is manufactured by plant B. Now we are given that probability that the machine is manufactured in plant A and the machine is of standard quality is given to us as 80% that can be written as 0.80 and the machine is of standard quality and is manufactured by machine 2 is given to us as 90% that is 0.90. Also probability that the machine is from plant A is 70% and probability that the machine is from plant B is given to us as 30%. Now we need to find out the probability that the standard machine has come out from plant A. So it will be equal to probability of plant A into probability of standard quality of a machine from plant A upon probability of plant A into probability of E upon plant A plus probability of plant B into probability of E upon plant B. Now what we need to do next is we need to just substitute these values from the given values that will be equal to 0.70 into 0.80 upon 0.70 into 0.80 plus 0.30 into 0.90. On simplifying we have 0.56 upon 0.83 which is further equal to 56 upon 83. So this is the required answer to the given question. I hope you have enjoyed the session. Bye and take care.