(A) (Rule of Total Probability) Two companies produce flashlights. Factory A's flashlights have a lifespan of over 5000 hours in 99% of cases, whereas factory B's flashlights have a lifespan for over 5000 hours in 95% of cases. It is known that factory A supplies 70% of the flashlights available and B supplies 30% of the total flashlights available. What is the chance that a purchased flashlight will work for longer than 5000 hours? (B) (Bayes' Rule): Compute the (conditional) probability that your flashlight came from factory A given that it lasted over 5000 hours.