 Hello friends and how are you all doing today? The question says the company has two plans to manufacture motorcycles 70% Motorcycles are manufactured at the first plant while 30% are manufactured at the second plant at the first plant 80% Motorcycles are rated of standard quality while at the second plant 90% are rated of standard quality a motorcycle randomly picked up is found to be of standard quality Find the probability That it has come out from the second so here suppose E1 E2 and A are the following events Event that is E1 event one be the event of choosing Plant one event two that is E2 be the event of choosing plant two and that event A be the event of picking up a motorcycle That is of standard Quality now we are given few probabilities. We are given that probability of Event one is 70 percent as 70 percent of the motorcycles are manufactured in Plant one whereas probability of E2 is 30 percent Also, we are given that probability that a motorcycle is of standard quality and it is from plant one is 80% whereas P of A upon E2 is equal to 90 percent we need to find that probability that The motorcycle that is picked up at random is of standard quality and it is chosen from plant two So now here on applying base theorem we have Probability of choosing plant two and picking up a motorcycle of standard quality will be equal to probability of choosing plant two into probability that a standard quality motorcycle is picked up from plant two Upon the total probability that is probability of E1 into probability of A upon E1 plus probability of E2 into probability of A upon E2 What we need to do further is we just need to substitute the values that are found out above so we have it as probability of E2 is 30% here it is 90% upon 70% into 80% 30% into 90% What we have done over here is we just have substituted the value that we have found out above that are also given to us in the question Just simplifying it now we have it as 2700 upon 10,000 whole upon 5600 upon 10,000 plus 2700 upon 10,000 Further we have 27 upon 100 upon Combining it we have it as 83 upon Simplifying it we have the answer to the given question as 27 upon 83 So this is the required answer that is this is the probability that The motorcycle that is randomly picked up is found to be of standard quality and it has come out from the second Plant right so this completes the session. Hope you understood it well to remember your base theorem and have a nice day