Each of the joints in a steel frame building has two welds. An inspector has determined that if the welds were done on Monday through Thursday (4/5 of the total) there is a 70% probability of no bad welds, a 20% probability of one bad weld, and a 10% probability of two bad welds. If the welds are done on Friday (1/5 of the total) there is a 50% probability of no bad welds, a 30% probability of one bad weld, and a 20% probability of two bad welds.
(a) What is the probability of a joint having one bad weld?
(b) If a joint has two bad welds, what is the probability that it was done on a Friday?