/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Texas hold 鈥檈m In the popular ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 4

Texas hold 鈥檈m In the popular Texas hold 鈥檈m variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your hand, the probability of getting four of a kind is 88/1000. (a) Explain what this probability means. (b) Why doesn鈥檛 this probability say that if you play 1000 such hands, exactly 88 will be four of a kind?

Short Answer

Expert verified
The probability of 88/1000 means there's an 8.8% chance per hand. It suggests an average outcome, not an exact count over trials, due to randomness.

Step by step solution

01

Understanding the Probability

The probability of 88/1000 means that in a single game of Texas hold 鈥檈m, if a player is holding a pair in their hand, the likelihood of forming "four of a kind" by drawing from the additional five shared cards is 88 out of 1000, or 8.8%.
02

Clarifying Probability Interpretation

Probability expresses how likely an event is to occur, not a guarantee. It represents the relative frequency of an event over a large number of trials.
03

Addressing the Misinterpretation of Probability

The probability of 88/1000 doesn't guarantee that in 1000 games, exactly 88 games will result in four of a kind. This is because probability deals with long-term tendencies and not exact outcomes in finite trials.
04

The Role of Randomness

Randomness implies that while we expect 88 of 1000 hands to be four of a kind on average, in practice, the actual count can vary due to chance.
05

Conclusion

Thus, while the probability suggests an average outcome, each individual hand is subject to random variation and won't precisely follow the probability in a finite number of games.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Texas hold 'em poker
Texas Hold 'em is a popular variant of poker involving strategy, skill, and some luck. In this game, each player is dealt two private cards, known as 'hole cards'. Players then use these along with five community cards to form the best possible five-card poker hand. The game unfolds over several betting rounds, providing players opportunities to bet, fold, or wait for more community cards. The strategic aspect comes from the fact that players have to read their opponents and make decisions based on incomplete information. They must balance risk with the potential reward, making Texas Hold 'em both exciting and challenging to master.
Four of a kind
A "Four of a Kind" is a strong poker hand that occurs when a player has four cards of the same rank, combined with any fifth card. When evaluating this hand, its strength is quite formidable and is usually only beaten by a straight flush or a royal flush. In the context of the exercise, achieving a four of a kind while starting with a pair involves a probability angle, where players must also consider the community cards. Understanding the likelihood of completing such a hand is key to strategic decision-making in Texas Hold 'em.
Randomness in probability
Randomness is a core principle in probability and plays a significant role in Texas Hold 'em. Each game is a mix of deliberate player strategies and the chance-based nature of card distribution. A player may hope for a certain card to complete a hand but must rely on probability to assess the likelihood of receiving it. Randomness ensures that no two games are exactly alike, and any outcome is theoretically possible given enough plays. This variability colors the player's experience, making poker not just about the hands you鈥檙e dealt, but how you navigate the uncertainty of what others might have.
Probability interpretation
Probability can be interpreted as a measure of how likely an event is to occur. In the context of poker, it quantifies expectations rather than guarantees. The given probability of 88/1000 for obtaining a four of a kind while initially holding a pair doesn't mean that this event will precisely occur 88 times in 1000 games. Instead, it is a statistical expectation over a large number of trials. Outcomes in the short term can vary widely due to randomness, and players must understand that probability provides guidance over long averages rather than certainties in individual hands.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Exercises 33 to 35 refer to the following setting. A basketball player makes 47% of her shots from the field during the season. You want to estimate the probability that the player makes 5 or more of 10 shots. You simulate 10 shots 25 times and get the following numbers of hits: 5754153434534463417455657 What is your estimate of the probability? (a) 5/25, or 0.20 (b) 11/25, or 0.44 (c) 12/25, or 0.48 (d) 16/25, or 0.64 (e) 19/25, or 0.76

Teens online We saw in an earlier example (page 319) that 93% of teenagers are online and that 55% of online teens have posted a profile on a social-networking site. Of online teens with a profile, 76% have placed comments on a friend鈥檚 blog. What percent of all teens are online, have a profile, and comment on a friend鈥檚 blog? Show your work.

Rolling dice Suppose you roll two fair, six-sided dice鈥攐ne red and one green. Are the events sum is 8 and green die shows a 4 independent? Justify your answer.

Urban voters The voters in a large city are 40% white, 40% black, and 20% Hispanic. (Hispanics may be of any race in official statistics, but here we are speaking of political blocks.) A mayoral candidate anticipates attracting 30% of the white vote, 90% of the black vote, and 50% of the Hispanic vote. Draw a tree diagram to represent this situation. What percent of the overall vote does the candidate expect to get? Use the four-step process to guide your work.

MySpace versus Facebook A recent survey suggests that 85% of college students have posted a profile on Facebook, 54% use MySpace regularly, and 42% do both. Suppose we select a college student at random. (a) Assuming that there are 20 million college students, make a two-way table for this chance process. (b) Construct a Venn diagram to represent this setting. (c) Consider the event that the randomly selected college student has posted a profile on at least one of these two sites. Write this event in symbolic form using the two events of interest that you chose in (b). (d) Find the probability of the event described in (c). Explain your method.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.