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Unformatted text preview: Chapter 3 Probability 3.1 Introduction to Probability via Poker and Roulette Cards • Poker is a card game played with the standard 52 card deck. • There are 4 suits: hearts, diamonds, clubs, and spades. • Hearts and diamonds are red; clubs and spades are black. • Each suit has thirteen cards. • Each suit consists of cards labeled 2 through 10, followed by jack, queen, king, and ace. • Face cards are the jack, queen, and king; and picture cards are jack, queen, kind, and ace. • There are many variations of Poker. • Games include, 5 card draw poker, 7 card stud poker, blackjack, Texas Hold’em. Example 1: If you were to deal twentysix card from a complete deck (without jokers), approximately how many cards do you think would be black? Approximately how many do you think would be jacks, queens, or kings? Example 2: How many hearts are there in a deck of cards? What fraction of a deck is hearts? Example 3: How many jacks are there in a deck of cards? What fraction of a deck is jacks? 32 Example 4: How many ways to choose 5 cards? Example 5: How many ways to choose 5 hearts? Example 6: How many ways to choose 1 heart and 1 spade? Example 7: How many ways to choose 3 hearts and 2 spades? Roulette The American roulette wheel has 38 numbered compartments around its circumference. 36 of these compart ments are number from 1 to 36 and are colored red(18) or black(18). The remaining two are numbered 0 and 00 and are colored green. Players place their bets by putting their chips on an appropriate spot on the roulette table. The dealer spins the wheel and then drops a ball onto the spinning wheel. The ball eventually comes to rest in one of the compartments, and that compartment’s number is the winning number. Example 8: Find the outcome of each bet. 1. You bet $15 on the 20 and the ball lands on the 20. 2. You bet $30 on the odd numbers and the ball lands on 3. 3. You bet $25 on the 112 section and the ball lands on the number 13. 4. You bet $20 on the 16171920 square. 33 Example 9: How much must you bet on a twonumber split to be able to win at least $100? (Bets must be in $1 increments) What’s the probability got to do with it? • Probability is the study of the likelihood of an event. • People who play cards or table games need to know the probability of an event in order to make informed decisions. 34 3.2 Basic Terms of Probability Definition. An experiment is a process by which an observation, or outcome, is obtained Definition. A sample space is the set S of all possible outcomes of an experiment. Definition. An event is any subset E of the sample space S . Example 1 : If a single die is rolled, • The experiment is the rolling of the die....
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 Summer '08
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 Math, Probability

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