QuestionQuestion

In the mail room of a university office, a stream of blue and yellow mail carts pass a mail sorting robot. Blue carts contain 7 domestic letters for every 3 international letters. Yellow carts contain 2 domestic letters for every 3 international letters. Blue carts are followed by blue carts 70% of the time, but 30% of the time they are followed by a yellow cart. Yellow carts are followed by yellow carts half of the time, and the other half of the time they are followed by a blue cart. The first cart, every morning, is yellow 9 of every 10 times. The robot pulls a single letter from each cart as the cart passes it by.

1. Draw a markov model to represent the joint distribution over cart colors and the origins of letters selected by the robot. Include a conditional probability table (CPT) with each variable in your model.

2. What is the probability that the first three letters selected by the robot, in order, will be: domestic, international, domestic?

3. What is the probability that the fourth cart will be blue if the first three letters selected, in order, are: international, international, domestic?

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