In a remote tropical region, there is a direct road from A to B but it is impassable about 50% of the time due to rain. An alternative route passes through a third location C. Suppose the road from A to C is passable 75% of the time, while the road from C to B is passable 70% of the time. Also, from past experience, if the road from A to C is passable, then the road from C to B is passable 80% of the time, and if the route from A to C to B is passable, then the direct route from A to B also has an 80% chance of being passable.
a) State the information given in the question in probability notation.
b) What is the probability a traveller can get from A to B?
c) A traveller journeys from A to C and stays overnight. During the night, rain makes the road from A to C impassable. What is the probability the traveller can still get from C to B?