An electric wheelchair has been designed for disabled people to move around. It is installed with a robot-controlled joystick, which is designed to work 80% of the time. However, this probability varies with different moving directions. Consider the following scenario. From a certain location in a room, a wheelchair user will either (1) turn sharply to the left and navigate through a door (denoted as event D), (2) proceed straight to the other side of the room (denoted as event S), or (3) turn slightly right and stop at a table(denoted as event T). Among those tests where the joystick worked well, the user moved to the door 10% of the time, moved straight 80% of the time, and moved to the table 10% of the time. When the joystick failed to function, the user moved to the door 70% of the time, moved straight 20% of the time, and moved to the table 10% of the time. (a) What is the probability that a user moves toward the table and the joystick doesn't work?(5 marks)

(b) What are the probabilities that a user moves toward a table, straight, and toward the door, respectively? (6 marks) (c) Compute the probability that the joystick works well when a user moves to each of the three directions. Moving to which direction has the highest possibility that the joystick will work? (9 marks)