 Hello and welcome to the session that's work out the following problem. It says a company has two plans to manufacture TVs The first plant manufactures 70% of the TVs and the rest are manufactured by the other plant 80% of the TVs manufactured by the first plant are rated of standard quality While that of the second plant only 70% are of standard quality If a TV chosen at random is found to be of standard quality Find the probability that it was produced by the first plant. So, let's now move on to the solution and let E be the event of Choosing first plant since there are two plants To manufacture TV so E be the event of choosing first plant E2 is The event of choosing Second plant and A be the event of Choosing a TV of standard quality Since we have given that the Chosen TV is found to found to be of standard quality So a is the event of choosing a TV of standard quality. Now we are given that 70% of the TVs are manufactured by first plant so the probability of choosing the first plant is 70% that is 70 by 100 and the rest of the TVs are manufactured by the other plant So the probability of choosing the second plant is 30% that is 30 by 100 Now we are given that the 80% of the TVs chosen from the first plant Are of standard quality so the probability That the chosen which is of standard quality coming from the plant one that is probability of Standard TV That is TV of standard quality knowing that it is coming from the plant one is 80% that is 80 by 100 and probability of Choosing a TV of standard quality knowing that it is coming from plant two is 70% Since we are given that 70% of standard Quality TV are coming from the plant to its Probability 70% that is 70 by 100 now we have to find the probability that The TV found is Of standard quality we have to find the probability that it was chosen from the first plant That is we have to find probability of even given a that is TV chosen is found to be of Standard quality and That TV is coming from the first plant now we'll use the base theorem to find this So by base theorem probability of even given a is probability of even into probability of a given even upon probability of even into probability of a given even plus probability of e2 into probability of a Given even you must remember the base theorem now we'll substitute all the values in this now probability of even is 70 by 100 that is 7 by 10 Into a given even is 8 by 10 upon 7 by 10 into 8 by 10 Plus probability of e2 is 30 by 100 that is 3 by 10 Into probability of a given e2 that is 70 by 100 the 7 by 10 now this is 10 into 10 is 100 7 into 8 is 56 upon 56 upon 100 plus 21 upon 100 so now this is 56 upon 100 upon Here LCM would be 100 56 plus 21 is 77 So we have 56 by 100 into 100 by 77 Now 100 gets cancelled with 100 and we have 56 upon 77 so the probability of Choosing TV of standard quality from the first plant is 56 by 77 So this completes the question and the session why for now take care have a good day