Jim Alberts Question.An automatic machine in a small factory produces metal parts. Most of the time(90% by long records), it produces 95% good parts and the remaining have to bescrapped. Other times, the machine slips into a less productive mode and only produces70% good parts. The foreman observes the quality of parts that are producedby the machine and wants to stop and adjust the machine when she believes thatthe machine is not working well. Suppose that the first dozen parts produced aregiven by the sequences u s s s s s s s u s uwhere s satisfactory and u unsatisfactory.(a) After observing this sequence, what is the probability that the machine is in itsgood state?(b) If the foreman wishes to stop the machine when the probability of “good state”isunder 0.7, when should she stop