CIS630 Homework 5: Uncertainty & Decision Theory

Due: Must be submitted by May 27 at 11:59
1 point late penalty for each minute late

Submit instructions:

Write up all of your answers in a text editor so that it can be submitted electronically. Put all of the files you want to submit in a directory on STDSUN, and submit it using the command:

> submit c630aa lab5 (lab5_dir)

Where lab5_dir is the directory containing the files you want to submit.

  1. (35 points) You are playing Texas-hold'em poker. For the purposes of this problem, assume that you are the only person playing (not the usual case, but this simplifies things). You have two cards in your hand: an 8 of clubs and 6 of diamonds. There are three cards turned up on the table: 2 of clubs, king of hearts, and queen of spades. Two cards are face down on the table, and will be turned over one at a time.

    If you don't know the rules, in Texas-hold'em, you treat the cards in your hand and the cards on the table as one large hand. The deck is a standard 52-card deck (ranks 2,3,4,5,6,7,8,9,10,Jack,Queen,King,Ace in four suits: spades, hearts, diamonds, and clubs). A pair is two cards that have matching ranks (8 of spades, 8 of diamonds); three-of-a-kind are three cards with the same rank. These are the only relevant bits for the problem.

    1. What is the probability that the next card to be turned over will give you a pair?
    2. What is the probablity that when both cards are turned over, you will have one pair?
    3. What is the probablity that when both cards are turned over, you will have two pairs?
    4. What is the probablity that when both cards are turned over, you will have a three of a kind?
  2. (30 points) In baseball, two elements that contribute to whether you win or lose a game is whether you have good pitching and whether you have good batting. Consider the following table, which looks at the statistics for major league baseball games played this year (up to 5/19), presented as the joint probability of winning, pitching, and batting. To derive this data, each team was labeled as having "GoodPitching" or "BadPitching" and "GoodBatting" or "BadBatting". (In case you're interested, we derived this by looking at the ERA and batting average of the teams; half of the teams in the ranking were labeled "good" and half were "bad").

    Win Loses
    GoodPitching BadPitching GoodPitching BadPitching
    GoodBatting 0.150 0.111 0.112 0.124
    BadBatting 0.119 0.120 0.112 0.152

    1. What is the probability of a team having good pitching, bad batting, and winning a game? Write the answer as P(...)=###, where you fill in the ... and ### appropriately.
    2. What is the probability of a team winning a game given that they have good pitching and good batting? WARNING: this is not the same as the above question. Write the answer as P(...)=###, where you fill in the ... and ### appropriately.
    3. Almost all of the probabilities under losses are about the same. Is it true that as long as you don't have BadPitching and BadBatting, your chances of losing are about the same? Explain why or why not, supporting your answers with probabilities.

  3. (35 points) Do exercise 16.2 in the textbook.