Assignment 6: Probabilistic Reasoning
CSE 415: Introduction to Artificial Intelligence
The University of Washington, Seattle, Autumn 2012
Due Monday, November 19 through Catalyst CollectIt at 2:00 PM.

You should turn in a file A6.pdf containing your answers.

Reading material for this assignment is linked from our Textbook Information page.
Problems (Total: 50 points).
  1. (15 points) Compute the following probabilities.
    1. (3 points) Probability that a card drawn at random from a normal deck of 52 playing cards is either a queen, a heart, or a one-eyed jack.
    2. (5 points) Probability that a card drawn at random from a normal deck of 52 playing cards is a one-eyed jack, given that someone has looked at it and determined that it is either a heart or a jack.
    3. (7 points) Probability that a card drawn at random from a deck of special cards from a game G has a happy face on it, given that it also has a star on it, where the following class-conditional probabilities are given: The marginal probability of a happy face is P(H) = 0.2. The probability of a star given a happy face is P(S|H) = 0.75. The probability of a star given no happy face is P(S|~H) = 0.4.

     
  2. (5 points) Suppose that in a simulated horse race, the odds are 5 to 1 in favor of Baysy Daisy winning, and so the racetrack is paying at 1-5 or $2.40 back on a $2.00 wager. What is the probability with which Baysy Daisy is expected to win?
     
  3. (20 points) Recall the fact that the probabilities of a set of mutually exclusive outcomes that represent all the possibilites for a given event must sum to 1. Use it to fill in the gap in the following set of four probability values.

    A: It is snowing at 7 AM on a December morning in Slalom Pass.

    B: It is below 20 degrees Farenheit at 7 AM on a December morning in Slalom Pass.

    P(A^B)=0.4, P(A^~B)=0.2, P(~A^B)=0.3, P(~A^~B)=?.

    Now determine:

    P(A):

    P(B):

    P(A|B):

    P(B|A):

    Finally, show how Bayes' rule expresses P(B|A) in terms of the other values and check your value for P(B|A) by computing it that way.
     

  4. (10 points) In the Monty Hall problem, determine:
    1. (5 points) the probability of winning the car given that you don't (ever) switch your guess.
    2. (3 points) the probability of winning the car given that you do (always) switch your guess.
    3. (2 points) which strategy is more likely to win.
Updates and Corrections If necessary, updates and corrections will be posted here and mentioned in class or on the mailing list. This page was last updated Oct. 28, 2012.