Question: A production system has two production lines; each production line performs a two-[art process, and each process is completed by a different machine. Thus, there are four machines, which we can identify as two first-level machines and two second-level machines. Each of the first-level machines works properly 98% of the time, and each of the second-level machines works properly 96% of the time. All four machines are independent in regard to working properly or breaking down. Two products enter this production system, one in each production line.
a. Find the probability that both products successfully complete the two-part process (i.e. all four machines are working properly).
b. Find the probability that neither product successfully completes the two-part process (i.e. at least one of the machines in each production line is not working properly).