A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2, Problem 2.47P
Suppose that 5 of the numbers 1, 2,..., 14 are chosen. Find the probability that 9 is the third smallest value chosen.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
In a Poisson process with A = 500 arrivals per day, find the approximate probability that the thousandth
arrival comes between 47.5 and 48.5 hours after the start of observations.
Suppose you generate 300 independent observations X1, ..., X300 from a Uniform(0,3) distribution.
a) What is the approximate distribution of X?
b) What is the approximate probability that X is less than 1.57?
c) What is the approximate probability that the sum S300 = X₁++X300 is between 442 and
483?
Vehicles that cross a certain bridge have a mean weight of 4,675 pounds, with a standard deviation of
345 pounds. If there are 40 vehicles on the bridge at once, find the number a such that the (approximate)
probability is 99% that their combined weight does not exceed a.
Chapter 2 Solutions
A First Course in Probability (10th Edition)
Ch. 2 - A box contains 3 marbles: 1 red, 1 green, and 1...Ch. 2 - In an experiment, die is rolled continually until...Ch. 2 - Two dice are thrown. Let E be the event that the...Ch. 2 - A, B, and C take turns flipping a coin. The first...Ch. 2 - A system is composed of 5 components, each of...Ch. 2 - A hospital administrator codes incoming patients...Ch. 2 - Consider an experiment that consists of...Ch. 2 - Suppose that A and B are mutually exclusive events...Ch. 2 - A retail establishment accepts either the American...Ch. 2 - Sixty percent of the students at a certain school...
Ch. 2 - A total of 28 percent of American males smoke...Ch. 2 - An elementary school is offering 3 language...Ch. 2 - A certain town with a population of 100.000 has 3...Ch. 2 - The following data were given in a study of a...Ch. 2 - If it is assumed that all (525) poker hands are...Ch. 2 - Poker dice is played by simultaneously rolling 5...Ch. 2 - Twenty five people, consisting of 15 women and 10...Ch. 2 - Two cards are randomly selected from an ordinary...Ch. 2 - Two symmetric dice have had two of their sides...Ch. 2 - Suppose that you are playing blackjack against a...Ch. 2 - A small community organization consists of 20...Ch. 2 - Consider the following technique for shuffling a...Ch. 2 - A pair of fair dice is rolled. What is the...Ch. 2 - It two dice are rolled, what is the probability...Ch. 2 - A pair of dice is rolled until a sum of either 5...Ch. 2 - The game of craps is played as follows: A player...Ch. 2 - An urn contains 3 red and 7 black balls. Players A...Ch. 2 - An urn contains 5 red, 6 blue, and 8 green balls....Ch. 2 - An urn contains n white and m black balls, where n...Ch. 2 - The chess clubs of two schools consist of,...Ch. 2 - A 3-person basketball team consists of a guard, a...Ch. 2 - A group of individuals containing b boys and g...Ch. 2 - A forest contains 20 elk, of which 5 are captured,...Ch. 2 - The second Earl of Yarborough is reported to have...Ch. 2 - Seven balls are randomly withdrawn from an urn...Ch. 2 - Two cards are chosen at random from a deck of 52...Ch. 2 - An instructor gives her class a set of 10 problems...Ch. 2 - There are n socks. 3 of which are red, in a...Ch. 2 - There are 5 hotels in a certain town. If 3 people...Ch. 2 - If 4 balls are randomly chosen from an urn...Ch. 2 - If a die is rolled 4 times, what is the...Ch. 2 - Two dice are thrown n times in succession. Compute...Ch. 2 - a. If N people, including A and B, are randomly...Ch. 2 - Five people, designated as A, B, C, D, E, are...Ch. 2 - A woman has n keys, of which one will open her...Ch. 2 - How many people have to be in a room in order that...Ch. 2 - Suppose that 5 of the numbers 1, 2,..., 14 are...Ch. 2 - Given 20 people, what is the probability that...Ch. 2 - A group of 6 men and 6 women is randomly divided...Ch. 2 - In a hand of bridge, find the probability that you...Ch. 2 - Suppose that n balls are randomly distributed into...Ch. 2 - A closet contains 10 pairs of shoes. If 8 shoes...Ch. 2 - If 8 people, consisting of 4 couples, are randomly...Ch. 2 - Compute the probability that a bridge hand is void...Ch. 2 - Compute the probability that a hand of 13 cards...Ch. 2 - Two players play the following game: Player A...Ch. 2 - Prove the following relations: EFEEFCh. 2 - Prove the following relations: If EF, then FCEC.Ch. 2 - Prove the following relations: 3. F=FEFEC and...Ch. 2 - Prove the following relations: (1Ei)F=1EiF and...Ch. 2 - For any sequence of events E1,E2,..., define a new...Ch. 2 - Let E, F, and C be three events. Find expressions...Ch. 2 - Use Venn diagrams a. to simplify the expression...Ch. 2 - Prob. 2.8TECh. 2 - Suppose that an experiment is performed n times...Ch. 2 - Prove...Ch. 2 - If P(E)=.9 and P(F)=.8, show that P(EF).7. In...Ch. 2 - Show that the probability that exactly one of the...Ch. 2 - Prove that P(EF)=P(E)P(EF).Ch. 2 - Prove Proposition 4.4 by mathematical induction.Ch. 2 - An urn contains M white and N black balls. If a...Ch. 2 - Use induction to generalize Bonferronis inequality...Ch. 2 - Consider the matching problem. Example 5m, and...Ch. 2 - Let fn, denote the number of ways of tossing a...Ch. 2 - An urn contains n red and m blue balls. They are...Ch. 2 - Consider an experiment whose sample space consists...Ch. 2 - Consider Example 50, which is concerned with the...Ch. 2 - A cafeteria offers a three-course meal consisting...Ch. 2 - A customer visiting the suit department of a...Ch. 2 - A deck of cards is dealt out. What is the...Ch. 2 - Let A denote the event that the midtown...Ch. 2 - An ordinary deck of 52 cards is shuffled. What is...Ch. 2 - Urn A contains 3 red and 3 black balls, whereas...Ch. 2 - In a state lottery, a player must choose 8 of the...Ch. 2 - From a group of 3 first-year students, 4...Ch. 2 - For a finite set A, let N(A) denote the number of...Ch. 2 - Consider an experiment that consists of 6 horses,...Ch. 2 - A 5-card hand is dealt from a well-shuffled deck...Ch. 2 - A basketball team consists of 6 frontcourt and 4...Ch. 2 - Suppose that a person chooses a letter at random...Ch. 2 - Prove Booles inequality P(i=1Ai)i=1P(Ai)Ch. 2 - Show that if P(Ai)=1 for all i1, then P(i=1Ai)=1.Ch. 2 - Let Tk(n) denote the number of partitions of the...Ch. 2 - Five balls are randomly chosen, without...Ch. 2 - Four red, 8 blue, and 5 green balls are randomly...Ch. 2 - Ten cards are randomly chosen from a deck of 52...Ch. 2 - Balls are randomly removed from an urn initially...
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
- Suppose X1, X, are iid, each with some unknown distribution that has an expected value of μ = 25.7 and a standard deviation of σ = 4.3 a) if n = 50, find the approximate probability that the average X is less than 25. b) repeat part a for n = 100 and n 1,000 =arrow_forwardLet X1, ..., X10 be iid a) P(X < 7.5) ~ b) P(3.1 < x < 4.9) Normal(5, 90). Find the following probabilities for the sample mean X:arrow_forwardSuppose that X and Y are statistically independent and identically distributed uniform random variables on (0,1). (a) Write down the joint probability density function fx,y(x,y) of X and Y on its support. (b) The expression for the joint probability density function of the transformed random variables U=5X+Y and V=3X+2 Y on its support is: fu,v(u,v) = Au³ (C + D)E Which values of the constants A, B, C, D, E are correct (in the same order as they appear here)? ○ 1,8,1,8,1 ○ none of the answers is correct The joint probability density is constant on its support, hence B-C=0 and D=E=1, and A following from normalization. ○ 1/3, 1, 1.67, 1, -2 O 1/3, 1, 1.67, 1, 2 3, 1, 1.67, 1, -2arrow_forward
- Let us suppose that a particular lecturer manages, with probability 1, to develop exams that have mean 60 and standard deviation 19. The lecturer is teaching two classes, one of size 100 and the other one of size 36, and is about to give an exam to both classes. We treat all students as being independent. Give your answers below in three decimal places. (a) The approximate probability that the average test score in the class of size 100 exceeds 65 is (a), where is the cumulative distribution function of a standard normal random variable. Find the value of a. (b) The approximate probability that the average test score exceeds 65 in the class of size 36 is (B). Find the value of ẞ.arrow_forwardHINTS, ANSWERS, AND ETOOLS Home > CCG > Chapter 5 > Lesson 5.2.2 > Problem 5-69 CPM EDUCATIONAL PROGRAM CPN 5-69. The probability of winning $3 on the spinner at right is equal to the chance of winning $5. Find the expected value for one spin. Is this game fair? $3 ☐ Nint: $5 -$6 © 2022 CPM Educational Program. All rights reserved. 认arrow_forwardYoung's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 80 GPa and 2.5 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) ЛUSE SALT (a) Calculate P(79 ≤ X ≤ 81) when n = 9. (b) How likely is it that the sample mean diameter exceeds 81 when n = 25?arrow_forward
- In a sample of 176 students at an Australian university that introduced the use of plagiarism-detection software in a number of courses, 55 students indicated a belief that such software unfairly targets students. Does this suggest that a majority of students at the university do not share this belief? Test appropriate hypotheses at level 0.05. (Let p be the proportion of students at this university who do not share this belief.) USE SALT State the appropriate hypotheses. Ho: p = Ha 0.50 : p 0.50 Ho: p = 0.50 Ha: p > 0.50 Ho: p = 0.50 Ha: p 0.50 H₂: p = 0.50 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = What can you conclude? Do not reject the null hypothesis. There is not sufficient evidence that more than 50% of all students do not share the belief that the plagiarism-detection software unfairly targets students. Do not reject the null hypothesis. There is sufficient…arrow_forwardAn article described an investigation into the coating weights for large pipes resulting from a galvanized coating process. Production standards call for a true average weight of 200 lb per pipe. The accompanying descriptive summary and boxplot are from Minitab. N Variable ctg wt 30 Mean 206.27 Median TrMean 206.00 206.81 StDev 6.35 SEMean 1.16 Variable ctg wt Min 193.00 Max 218.00 Q1 202.75 Q3 212.00 190 200 210 220 Coating weight (a) What does the boxplot suggest about the status of the specification for true average coating weight? ○ It appears that the true average weight could be significantly off from the production specification of 200 lb per pipe. It appears that the true average weight is approximately 202 lb per pipe. ○ It appears that the true average weight is approximately 218 lb per pipe. ○ It appears that the true average weight is not significantly different from the production specification of 200 lb per pipe. (b) A normal probability plot of the data was quite…arrow_forwardThe following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions. 32.1 30.7 31.5 30.4 31.0 31.9 Л USE SALT The report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed. (a) Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using a = 0.01. State the appropriate hypotheses. Ho: μ # 30 Η ι μ 30 ○ Ho: μ = 30 Haμ 30 Ho: μ # 30 H₂ μ = 30 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = What can you conclude? ○ Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average stopping distance does exceed 30 ft. ◇ Reject the null hypothesis. There is sufficient evidence to conclude that the…arrow_forward
- An article reports the following values for soil heat flux of eight plots covered with coal dust. 37.9 35.2 37.9 37.2 35.3 28.5 18.1 24.1 USE SALT The mean soil heat flux for plots covered only with grass is 29.0. Assuming that the heat-flux distribution is approximately normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Test the appropriate hypotheses using α = 0.05. State the appropriate hypotheses. ○ Ho: μ = 29 Haμ 29 Ho: μ # 29 Ha: M = 29 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that there was an increase in mean heat flux. Do not reject the null hypothesis. There is sufficient evidence to conclude that there was an increase in mean heat flux. Reject the null hypothesis. There is not…arrow_forwardAn article describes an experiment in which several types of boxes were compared with respect to compression strength (lb). The table below presents the results of a single-factor ANOVA experiment involving I = 4 types of boxes. Type of Box Compression Strength (lb) Sample Mean Sample SD 1 655.5 788.3 734.3 721.4 679.1 699.4 713.00 46.55 2 789.2 772.5 786.9 686.1 732.1 774.8 756.93 40.34 3 4 737.1 639.0 696.3 671.7 717.2 727.1 535.1 628.7 542.4 559.0 586.9 520.0 698.07 562.02 37.20 39.87 USE SALT Suppose that the compression strength observations on the fourth type of box had been 645.1, 738.7, 652.4, 669.0, 696.9, and 630.0 (obtained by adding 110 to each previous X4;). Assuming no change in the remaining observations, carry out an F test with α = 0.05. State the appropriate hypotheses. O H0 μ₁ = μ₂ = μ3 = μ4 Ha at least two μ's are unequal O Ho: M₁ = μ₂ #M3 # M4 Ha at least two μs are equal Ho M1 M2 M3 = μ4 Ha all four μi's are unequal # Ho: M1 M2 M3 & M4 Ha: all four μ's are equal…arrow_forwardA shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µ; = E(X;) and σ, 2² = V(X;), suppose that the mean values and standard deviations are as follows: = 230 M1 °₁ = 11 M2 = 260 Из = 150 02 = 13 7 03 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume expected value variance ft³ ft6 = 27X1 + 125X2 + 512X3.] (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain. ○ The expected value would be correct, but the variance would not be correct. Neither the expected value nor the variance would be correct. Both the expected value and the variance would be correct. The expected value would not be correct, but the variance would be correct.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License