Question

 A robot-controlled joystick may be helpful for many disabled people as electric  wheelchairs are difficult to maneuver for many disabled people. From a certain location in  a room, a wheelchair user will either (1) turn sharply to the left and navigate through a  door, (2) proceed straight to the other side of the room, or (3) turn slightly right and stop at  a table. Denote these three events as D (for door), S (for other side of the room), and T (for  table). Based on the previous trips, P(D) = 0.5, P(S) = 0.2, P(T) = 0.3. The wheelchair is  installed with a robot-controlled joystick. When the user intends to go through the door, he  points the joystick straight 30% of the time; when the user intends to go straight, he points  the joystick straight 40% of the time; and, when the user intends to go to the table, he points  the joystick straight 5% of the time. If the wheelchair user points the joystick straight, what  is her most likely destination?

Answer 1

probabilities:

for door: $0.5\cdot0.3=0.15$

for other side of the room: $0.2\cdot0.4=0.08$

for table: $0.3\cdot0.05=0.015$

So, the most likely destination is the door (with max probability).