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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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