Can someone please show me how to solve this. Your help is greatly appreciated.

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

If I was being factious I would say the doctors office because they are having major cognitive ability problems. Also gender problems as the probabilities of actions are given for a male user, but the question is about a female user.

From a math stand point, the answer has to do with conditional probability. This is a simple multiplication in each case as we are given P(A) and P(B|A) for each case. We just multiply for each case.

For the male wheelchair user that we are given information about, if THAT person pointed their joystick straight , while in the fog of uncertainty the most probable outcome, based on prior behavior would be that they would be going to the door.

For a hypothetical female user, of which we have no additional information we could not make a prediction. Under the assumption she would point the control where she wanted to go, the answer would be straight. If we assume that she also has difficulties pointing in the right direction, we ould have no way of knowing where she is going.

Nice thought problem. Silly, but cute.

For those interested the final odds for Door:Straight:Table are 150:80:15