3. A robot is designed to do 2 tasks: sort colored bricks, and move balls into a
ID: 3051777 • Letter: 3
Question
3. A robot is designed to do 2 tasks: sort colored bricks, and move balls into a bucket.
Suppose variable X represents success in the brick task, and variable Y represents
success in the bucket task. The probabilities of success in this task are represented in
the following table.
X: sorting bricks
Success
Fail
Y: filling buckets
Success
0.45
0.25
Fail
0.20
0.10
a) Find P(X = success).
b) Find the probability the robot succeeds in filling the bucket, given that it has succeeded in
sorting the bricks.
c) Assign a value 1 to success and 0 to fail. Find the covariance of X and Y.
X: sorting bricks
Success
Fail
Y: filling buckets
Success
0.45
0.25
Fail
0.20
0.10
Explanation / Answer
a) P(X = success). = 0.45+0.20 = 0.65
b) P(robot succeeds in filling the bucket, given that it has succeeded in sorting the bricks.)
= 0.45/0.65
= 0.6923
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