1. Late for work Mrs Spring is a line manager of Andrew and Beth, working for the water company LIQUIDAQUA. She knows they both commute from the suburb of Peacefulwater in the south of the city, to the north where the company is based. Each employee drives their own car to work. (a) On some Monday morning, Beth calls Mrs Spring before work starts, to tell her that she will certainly be late for work, as there is an accident blocking the road. Mrs Spring thinks that if Beth is certain to be late for work, then it becomes quite likely that Andrew will also be late. Considering the two events that 'Beth is late' and 'Andrew is late', in terms of Mrs Spring's beliefs, would you describe them as dependent, independent, or conditionally independent? Briefly justify your answer. (b) After 3 months, on some Sunday evening, Mrs Spring finds out that on Monday morning works will be carried out on the road linking Peacefulwater and the company. She thinks it is very likely both Andrew and Beth are going to be late. The next morning Beth calls before the start of work to say that she will certainly be late. Mrs Spring thinks that she was right last night to expect this. Again, consider the two events that 'Beth is late and "Andrew is late? Would you best describe them, in terms of Mrs Spring's beliefs for the forthcoming Monday morning, as dependent, independent, or conditionally independent? Briefly justify your