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?

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Mathematics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats