Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1.3, Problem 8E
An urn contains 17 balls marked LOSE and three balls marked WIN. You and an opponent take turns selecting a single ball at random from the urn without replacement. The person who selects the third WIN ball wins the game. It does not matter who selected the first two WIN halls.
(a) If you draw first, find the
(b) If you draw first, find the probability that your opponent wins the game on his second draw.
(c) If you draw first, what is the probability that you win? HINE You could win on your second, third, fourth, or tenth draw, but not on your first.
(d) Would you prefer to draw first or second? Why?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Could you explain how the inequalities u in (0,1), we have 0 ≤ X ≤u-Y for any 0 ≤Y<u and u in (1,2), we either have 0 ≤ X ≤u-Y for any u - 1 < Y<1, or 0≤x≤1 for any 0 ≤Y≤u - 1 are obtained please. They're in the solutions but don't understand how they were derived.
Can you please explain how to find the bounds of the integrals for X and Y and also explain how to find the inequalites that satisfy X and Y. I've looked at the solutions but its not clear to me on how the inequalities and bounds of the integral were obtained. If possible could you explain how to find the bounds of the integrals by sketching a graph with the region of integration. Thanks
QUESTION 18 - 1 POINT
Jessie is playing a dice game and bets $9 on her first roll. If a 10, 7, or 4 is rolled, she wins $9. This happens with a probability of . If an 8 or 2 is rolled, she loses her $9. This has a probability of J. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on her first roll.
Round to the nearest cent if necessary. Do not round until the final calculation.
Provide your answer below:
Chapter 1 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 1.1 - Of a group of patients having injuries, 28% visit...Ch. 1.1 - An insurance company looks at its auto insurance...Ch. 1.1 - Draw one card at random from a standard deck of...Ch. 1.1 - A fair coin is tossed four times, and the sequence...Ch. 1.1 - Consider the trial on which a 3 is first observed...Ch. 1.1 - If P(A)=0.5,P(B)=0.6, and P(AB)=0.4, find (a)...Ch. 1.1 - Given that P(AB)=0.76 and P(AB)=0.87, find P(A).Ch. 1.1 - During a visit to a primary care physicians...Ch. 1.1 - Roll a fair six-sided die three times. Let...Ch. 1.1 - Prove Theorem 1.1-6.
Ch. 1.1 - A typical roulette wheel used in a casino has 38...Ch. 1.1 - Let x equal a number that is selected randomly...Ch. 1.1 - Divide a line segment into two parts by selecting...Ch. 1.1 - Let the interval [r,r] be the base of a...Ch. 1.1 - Let S=A1A2...Am, where events A1,A2,...,Am are...Ch. 1.1 - Let pn,n=0,1,2..., be the probability that an...Ch. 1.2 - A boy found a bicycle lock for which the...Ch. 1.2 - In designing an experiment, the researcher can...Ch. 1.2 - How many different license plates are possible if...Ch. 1.2 - The eating club is hosting a make-your-own sun-dae...Ch. 1.2 - How many four-letter code words are possible using...Ch. 1.2 - Suppose that Novak Djokovic and Roger Federer are...Ch. 1.2 - In a state lottery, four digits are drawn at...Ch. 1.2 - How many different varieties of pizza can be made...Ch. 1.2 - The World Series in baseball continues until...Ch. 1.2 - Pascals triangle gives a method for calculating...Ch. 1.2 - Three students (S) and six faculty members (F) are...Ch. 1.2 - Prove: r=0n(1)r(nr)=0andr=0n(nr)=2n HINT: Consider...Ch. 1.2 - A bridge hand is found by taking 13 cards at...Ch. 1.2 - At the end of a semester, 29 students in a...Ch. 1.2 - Prove Equation 1.2-2. HINT: First selectn1...Ch. 1.2 - A box of candy hearts contains 52 hearts, of which...Ch. 1.2 - A poker hand is defined as drawing five cards at...Ch. 1.3 - A common screening test for 1-IIV is called the...Ch. 1.3 - The following table classifies 1456 people by...Ch. 1.3 - Let A1 and A2 be the events that a person is left-...Ch. 1.3 - Two cards are drawn successively and without...Ch. 1.3 - Suppose that the gene for eye color for a certain...Ch. 1.3 - A researcher finds that, of 982 men who died in...Ch. 1.3 - An urn contains four colored halls: two orange and...Ch. 1.3 - An urn contains 17 balls marked LOSE and three...Ch. 1.3 - An urn contains four balls numbered 1 through 4....Ch. 1.3 - A single card is drawn at random from each of six...Ch. 1.3 - Consider the birthdays of the students in a class...Ch. 1.3 - You are a member of a class of 18 students. A bowl...Ch. 1.3 - In the gambling game craps. two dice are rolled...Ch. 1.3 - Some albatrosses return to the worlds only...Ch. 1.3 - An urn contains eight red and seven blue balls. A...Ch. 1.3 - Bowl A contains three red and two white chips, and...Ch. 1.4 - Let A and B be independent events with P(A)=0.7...Ch. 1.4 - Let P(A)=0.3 and P(B)=0.6. (a) Find P(AB) when A...Ch. 1.4 - Let A and B be independent events with P(A)=14 and...Ch. 1.4 - Prove parts (b) and (c) of Theorem 1.4-1.Ch. 1.4 - If P(A)=0.8,P(B)=0.5, and P(AB)=0.9, are A and B...Ch. 1.4 - Show that if A, B, and C are mutually independent,...Ch. 1.4 - Each of three football players will attempt to...Ch. 1.4 - Die A has orange on one face and blue on five...Ch. 1.4 - Suppose that A, B, and C are mutually independent...Ch. 1.4 - Let D1,D2,D3 be three four-sided dice whose sides...Ch. 1.4 - Let A and B be two events. (a) If the events A and...Ch. 1.4 - Flip an unbiased coin five independent times....Ch. 1.4 - An urn contains two red balls and four white...Ch. 1.4 - In Example 1.4-5, suppose that the probability of...Ch. 1.4 - An urn contains ten red and ten white balls. The...Ch. 1.4 - An urn contains five balls, one marked WIN and...Ch. 1.4 - Each of the 12 students in a class is given a fair...Ch. 1.4 - An eight-team single-elimination tournament is set...Ch. 1.4 - Extend Example 1.4-6 to an n-sided die. That is,...Ch. 1.4 - Hunters A and B shoot at a target with...Ch. 1.5 - Bowl B1 contains two white chips, bowl B2 contains...Ch. 1.5 - Bean seeds from supplier A have an 85% germination...Ch. 1.5 - A doctor is concerned about the relationship...Ch. 1.5 - Assume that an insurance company knows the...Ch. 1.5 - At a hospitals emergency room, patients are...Ch. 1.5 - A life insurance company issues standard,...Ch. 1.5 - A chemist wishes to detect an impurity in a...Ch. 1.5 - A store sells four brands of tablets. The least...Ch. 1.5 - There is a new diagnostic test for a disease that...Ch. 1.5 - Prob. 10ECh. 1.5 - At the beginning of a certain study of a group of...Ch. 1.5 - A test indicates the presence of a particular...Ch. 1.5 - A hospital receives 40% of its flu vaccine from...Ch. 1.5 - Two processes of a company produce rolls of...
Additional Math Textbook Solutions
Find more solutions based on key concepts
1. How much money is Joe earning when he’s 30?
Pathways To Math Literacy (looseleaf)
153. A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure, the edges ...
College Algebra (7th Edition)
True or False The quotient of two polynomial expressions is a rational expression, (p. A35)
Precalculus
(a) Make a stem-and-leaf plot for these 24 observations on the number of customers who used a down-town CitiBan...
APPLIED STAT.IN BUS.+ECONOMICS
147. Draining a tank Water drains from the conical tank shown in the accompanying figure at the rate .
a. What...
University Calculus
23. A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $120 from the gro...
College Algebra (Collegiate Math)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- 5 of 5 (i) Let a discrete sample space be given by Ω = {ω1, 2, 3, 4}, Total marks 12 and let a probability measure P on be given by P(w1) 0.2, P(w2) = 0.2, P(w3) = 0.5, P(w4) = 0.1. = Consider the random variables X1, X2 → R defined by X₁(w3) = 1, X₁(4) = 1, X₁(w₁) = 1, X₁(w2) = 2, X2(w1) = 2, X2(w2) = 2, X2(W3) = 1, X2(w4) = 2. Find the joint distribution of X1, X2. (ii) [4 Marks] Let Y, Z be random variables on a probability space (N, F, P). Let the random vector (Y, Z) take on values in the set [0,1] × [0,2] and let the joint distribution of Y, Z on [0,1] × [0,2] be given by 1 dPy,z(y, z) (y²z + y²²) dy dz. Find the distribution Py of the random variable Y. [8 Marks]arrow_forwardTotal marks 16 5. Let (,,P) be a probability space and let X : → R be a random variable whose probability density function is given by f(x) = }}|x|e¯|×| for x Є R. (i) (ii) Find the characteristic function of the random variable X. [8 Marks] Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1, 2. (iii) What is the variance of X? [6 Marks] [2 Marks]arrow_forwardTotal marks 16 5. Let (N,F,P) be a probability space and let X : N → R be a random variable such that the probability density function is given by f(x)=ex for x € R. (i) Find the characteristic function of the random variable X. [8 Marks] (ii) Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1,2. (iii) What is the variance of X. [6 Marks] [2 Marks]arrow_forward
- 6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]arrow_forward6. Let X be a random variable taking values in (0,∞) with proba- bility density function fx(u) = 5e5u u > 0. Total marks 8 Let Y = X2. Find the probability density function of Y. [8 Marks]arrow_forward5. Let a probability measure P on ([0,3], B([0,3])) be given by 1 dP(s): = ½ s² ds. 9 Consider a random variable X : [0,3] → R given by X(s) = s², sc [0,3]. S Total marks 7 Find the distribution of X. [7 Marks]arrow_forward
- Problem: The probability density function of a random variable is given by the exponential distribution Find the probability that f(x) = {0.55e−0.55x 0 < x, O elsewhere} a. the time to observe a particle is more than 200 microseconds. b. the time to observe a particle is less than 10 microseconds.arrow_forwardProblem: The probability density function of a random variable is given by the exponential distribution Find the probability that f(x) = {0.55e-0.55 x 0 < x, O elsewhere} a. the time to observe a particle is more than 200 microseconds. b. the time to observe a particle is less than 10 microseconds.arrow_forwardUnknown to a medical researcher, 7 out of 24 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 4 patients will die? Express as a fraction or a decimal number rounded to four decimal places.arrow_forward
- Was wanting to check if my calculations were correct Suppose 52% of the population has a college degree. If a random sample of size 808 is selected, what is the probability that the proportion of persons with a college degree will be less than 54%? Round to four decimal places. after following the formula I got 0.8724arrow_forwardAt the beginning of each semester, students at the University of Minnesota receive one prepaid copy card that allows them to print from the copiers and printers on campus. The amount of money remaining on the card can be modeled by a linear equation where A represents how much remains on the card (in dollars) and p represents the number of pages that the student has printed. The graph of this linear equation is given below. 100 90 80 70 60 50 40 30 20 10 0 A = Amount on Card ($) 0 200 400 600 800 1000 1200 1400 1600 p = Number of Pages Printed What information does the vertical intercept tell you (represent) for this problem? Be sure to include specific details in your answer -- your answer should have both quantitative and qualitative data to describe the answer in terms of the question.arrow_forwardData management no 2 thanksarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Bayes' Theorem 1: Introduction and conditional probability; Author: Dr Nic's Maths and Stats;https://www.youtube.com/watch?v=lQVkXfJ-rpU;License: Standard YouTube License, CC-BY
What is Conditional Probability | Bayes Theorem | Conditional Probability Examples & Problems; Author: ACADGILD;https://www.youtube.com/watch?v=MxOny_1y2Q4;License: Standard YouTube License, CC-BY
Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=OByl4RJxnKA;License: Standard YouTube License, CC-BY
Bayes' Theorem - The Simplest Case; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XQoLVl31ZfQ;License: Standard Youtube License