/*! 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} Q. 7 An unenlightened gamblera. A gam... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 7 (page 309)

An unenlightened gambler

a. A gambler knows that red and black are equally likely to occur on each spin of a

roulette wheel. He observes that 5 consecutive reds have occurred and bets heavily on

black at the next spin. Asked why, he explains that 鈥渂lack is due.鈥� Explain to the

gambler what is wrong with this reasoning.

b. After hearing you explain why red and black are still equally likely after 5reds on the

roulette wheel, the gambler moves to a card game. He is dealt 5straight red cards from

a standard deck with26red cards and 26black cards. He remembers what you said and

assumes that the next card dealt in the same hand is equally likely to be red or black.

Explain to the gambler what is wrong with this reasoning.

Short Answer

Expert verified

a) Each spin is independent, receiving red and black has the same probability even after you know five reds have occurred.

b)No, because five red cards have already been eliminated from the card deck, leaving the deck with more black than red cards.

Step by step solution

01

Part (a) Step 1: Given information

We have to tell what is wrong with this reasoning.

02

Part (a) Step 2: Explanation

Because each spin is independent, receiving red and black has the same probability even after you know five reds have occurred. As a result, red has a 50% probability of winning, and black has a 50% chance of winning.

03

Part (b) Step 1: Given information

We have to explain to the gambler what is wrong with this reasoning.

04

Part (b) Step 2: Explanation

No, because five red cards have already been eliminated from the card deck, leaving the deck with more black than red cards.

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!

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

Languages in Canada Canada has two official languages, English and French. Choose a Canadian at random and ask, 鈥淲hat is your mother tongue?鈥� Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region

a. Explain why this is a valid probability model.

b. What is the probability that the chosen person鈥檚 mother tongue is not English?

c. What is the probability that the chosen person鈥檚 mother tongue is one of Canada鈥檚 official languages?

BMI (2.2, 5.2, 5.3) Your body mass index (BMI) is your weight in kilograms divided by

the square of your height in meters. Online BMI calculators allow you to enter weight in

pounds and height in inches. High BMI is a common but controversial indicator of being

overweight or obese. A study by the National Center for Health Statistics found that the

BMI of American young women (ages 20 to 29) is approximately Normally distributed

with mean 26.8 and standard deviation 7.4.

27

a. People with BMI less than 18.5 are often classed as 鈥渦nderweight.鈥� What percent of

young women are underweight by this criterion?

b. Suppose we select two American young women in this age group at random. Find the

probability that at least one of them is classified as underweight.

Colorful disksA jar contains 36disks: 9each of four colors鈥攔ed, green, blue, and Page Number: 328yellow. Each set of disks of the same color is numbered from 1to 9. Suppose you draw one disk at random from the jar. Define events R: get a red disk, and N: get a disk with the number 9.

a. Make a two-way table that describes the sample space in terms of events Rand N.

b. Find P(R)and P(N).

c. Describe the event 鈥�Rand N鈥� in words. Then find the probability of this event.

d. Explain why P(RorN)鈮�P(R)+P(N) Then use the general addition rule to computeP(RorN).

Mac or PC? A recent census at a major university revealed that60%of its students mainly used Macs. The rest mainly used PCs. At the time of the census, 67%of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23%of respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census. Define events G: is a graduate student and M: primarily uses a Mac.

a. Find P(G 鈭� M). Interpret this value in context.

b. Consider the event that the randomly selected student is an undergraduate student and

primarily uses a PC. Write this event in symbolic form and find its probability.

Body image A random sample of 1200U.S. college students was asked, 鈥淲hat is your perception of your own body? Do you feel that you are overweight, underweight, or about right?鈥� The two-way table below summarizes the data on perceived body image by gender.

Suppose we randomly select one of the survey respondents.

a. Given that the person perceived his or her body image as about right, what鈥檚 the

probability that the person is female?

b. If the person selected is female, what鈥檚 the probability that she did not perceive her body image as overweight?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied 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.