A computer system is designed so that if component c1 fails, it is bypassed and :2 is used. If :2 fails, then it is bypassed and component c3 is used. If :3 fails, then it is bypassed and Component c4 is used. The system fails only if all 4 components fall. The failure of any of the four components is independent or the failure ofany or the other components. There is a .4 probability that c1 fails, a .4 probability that c2 fails, a .3 probability that c3 fails and a .2 probability that (:4 fails a. What is the probability C1, C2, C3, and C4 all fail? b. what is the probability none of c1, c2, c3, or CA fail' c. what is the probability that the system works (does not fall)? d. What is the probability that Cl and C3 fail7 . What is the probability that C1 or C3 fails? f. What is the probability that exactly one of the components works? Add any comments below. to \\\\