A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 3, Problem 3.62P
Barbara and Dianne go target shooting Suppose that each of Barbara’s shots hits a wooden duck target with
a. both shots hit the duck?
b. Barbara’s shot hit the duck?
What independence assumptions have you made?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
A First Course in Probability
Ch. 3 - Two fair dice are rolled. What is the conditional...Ch. 3 - If two fair dice are rolled, what is the...Ch. 3 - Use Equation (2.1) to compute in a hand of bridge...Ch. 3 - What is the probability that at least one of a...Ch. 3 - An urn contains 6 white and 9 black balls. If 4...Ch. 3 - Consider an urn containing 12 balls, of which 8...Ch. 3 - The king comes from a family of 2 children. What...Ch. 3 - A couple has 2 children. What is the probability...Ch. 3 - Consider 3 urns. Urn A contains 2 white and 4 red...Ch. 3 - Three cards are randomly selected, without...
Ch. 3 - Two cards are randomly chosen without replacement...Ch. 3 - A recent college graduate is planning to take the...Ch. 3 - Suppose that an ordinary deck of 52 cards (which...Ch. 3 - An urn initially contains 5 white and 7 black...Ch. 3 - An ectopic pregnancy is twice as likely to develop...Ch. 3 - Ninety-eight percent of all babies survive...Ch. 3 - In a certain community, 36 percent of the families...Ch. 3 - A total of 46 percent of the voters in a certain...Ch. 3 - A total of 4.8 percent of the women and 37 percent...Ch. 3 - Fifty-two percent of the students at a certain...Ch. 3 - A total of 500 married working couples were polled...Ch. 3 - A red die, a blue die, and a yellow die (all six...Ch. 3 - Urn I contains 2 white and 4 red balls, whereas...Ch. 3 - Each of 2 balls is painted either black or gold...Ch. 3 - The following method was proposed to estimate the...Ch. 3 - Suppose that 5 percent of men and 0.25 percent of...Ch. 3 - All the workers at a certain company drive to work...Ch. 3 - Suppose that an ordinary deck of 52 cards is...Ch. 3 - There are 15 tennis balls in a box, of which 9...Ch. 3 - Consider two boxes, one containing 1 black and 1...Ch. 3 - Ms. Aquina has just had a biopsy on a possibly...Ch. 3 - A family has j children with probability pj, where...Ch. 3 - On rainy days, Joe is late to work with...Ch. 3 - In Example 31, suppose that the new evidence is...Ch. 3 - With probability .6, the present was hidden by...Ch. 3 - Stores A, B, and C have 50, 75, and 100 employees,...Ch. 3 - a. A gambler has a fair coin and a two-headed coin...Ch. 3 - Urn A has 5 white and 7 black balls. Urn B has 3...Ch. 3 - In Example 3a, what is the probability that...Ch. 3 - Consider a sample of size 3 drawn in the following...Ch. 3 - A deck of cards is shuffled and then divided into...Ch. 3 - Twelve percent of all U.S. households are In...Ch. 3 - There are 3 coins in a box. One is a two-headed...Ch. 3 - Three prisoners are informed by their jailer that...Ch. 3 - Suppose we have 10 coins such that if the ith coin...Ch. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - Each of 2 cabinets identical n appearance has 2...Ch. 3 - Prostate cancer is the most common type of cancer...Ch. 3 - Suppose that an insurance company classifies...Ch. 3 - A worker has asked her supervisor for a letter of...Ch. 3 - A high school student is anxiously waiting to...Ch. 3 - A parallel system functions whenever at least one...Ch. 3 - If you had to construct a mathematical model for...Ch. 3 - In a class, there are 4 first-year boys, 6...Ch. 3 - Suppose that you continually collect coupons and...Ch. 3 - A simplified model for the movement of the price...Ch. 3 - Suppose that we want to generate the outcome of...Ch. 3 - Independent flips of a coin that lands on heads...Ch. 3 - The color of a persons eyes is determined by a...Ch. 3 - Genes relating to albinism are denoted by A and a....Ch. 3 - Barbara and Dianne go target shooting Suppose that...Ch. 3 - A and B are involved in a duel. The rules of the...Ch. 3 - A true - false question is to be posed to a...Ch. 3 - Assume, as in Example 3h, that 64 percent of twins...Ch. 3 - The probability of the closing of the ith relay in...Ch. 3 - An engineering system consisting of n components...Ch. 3 - In Problem 3.70a, find the conditional probability...Ch. 3 - A certain organism possesses a pair of each of 5...Ch. 3 - There is a 50—50 chance that the queen carries...Ch. 3 - On the morning of September 30, 1982, the...Ch. 3 - A town council of 7 members contains a steering...Ch. 3 - Suppose that each child born to a couple is...Ch. 3 - A and B alternate rolling a pair of dice, stopping...Ch. 3 - In a certain village, it is traditional for the...Ch. 3 - Prob. 3.76PCh. 3 - Consider an unending sequence of independent...Ch. 3 - A and B play a series of games. Each game is...Ch. 3 - In successive rolls of a pair of fair dice, what...Ch. 3 - In a certain contest, the players are of equal...Ch. 3 - An investor owns shares in a stock whose present...Ch. 3 - A and B flip coins. A starts and continues...Ch. 3 - Die A has 4 red and 2 white faces, whereas die B...Ch. 3 - An urn contains 12 balls, of which 4 are white....Ch. 3 - Repeat Problem 3.87 when each of the 3 players...Ch. 3 - Let S={1,2,...,n} and suppose that A and B are,...Ch. 3 - Consider Example 2a, but now suppose that when the...Ch. 3 - In Example 5, what is the conditional probability...Ch. 3 - In Laplace s rule of succession (Example 5e ), are...Ch. 3 - A person tried by a 3-judge panel is declared...Ch. 3 - Suppose that n independent trials, each of which...Ch. 3 - Show that if P(A)0, then P(ABA)P(ABAB)Ch. 3 - Prob. 3.2TECh. 3 - Consider a school community of m families, with ni...Ch. 3 - A ball is in any one of n boxes and is in the ith...Ch. 3 - a. Prove that if E and F are mutually exclusive,...Ch. 3 - Prove that if E1,E2,...,En are independent events,...Ch. 3 - a. An urn contains n white and m black balls. The...Ch. 3 - Let A, B, and C, be events relating to the...Ch. 3 - Consider two independent tosses of a fair coin....Ch. 3 - Two percent of women age 45 who participate in...Ch. 3 - In each of n independent tosses of a coin, the...Ch. 3 - Show that 0ai1,i=1,2,..., then...Ch. 3 - The probability of getting a head on a single toss...Ch. 3 - Suppose that you are gambling against an...Ch. 3 - Independent trials that result in a success with...Ch. 3 - Prob. 3.16TECh. 3 - Prob. 3.17TECh. 3 - Let Q. denote the probability that no run of 3...Ch. 3 - Consider the gamblers ruin problem, with the...Ch. 3 - Prob. 3.20TECh. 3 - The Ballot Problem. In an election, candidate A...Ch. 3 - As a simplified model for weather forecasting,...Ch. 3 - A bag contains a white and b black balls. Balls...Ch. 3 - A round-robin tournament of n contestants is a...Ch. 3 - Prove directly thatP(EF)=P(EFG)P(GF)+P(EFGC)P(GCF)Ch. 3 - Prove the equivalence of Equations (5.11) and...Ch. 3 - Prob. 3.27TECh. 3 - Prove or give a counterexample, if E1 and E2 are...Ch. 3 - In Laplaces rule of succession (Example 5e ), show...Ch. 3 - In Laplaces rule of succession (Example 5e),...Ch. 3 - Prob. 3.31TECh. 3 - In a game of bridge, West has no aces What is the...Ch. 3 - Prob. 3.2STPECh. 3 - How can 20 balls, 10 white and 10 black, be put...Ch. 3 - Prob. 3.4STPECh. 3 - An urn has r red and w white balls that are...Ch. 3 - An urn contains b black balls and r red balls. One...Ch. 3 - A friend randomly chooses two cards, without...Ch. 3 - Show that P(HE)P(GE)=P(H)P(G)P(EH)P(EG). Suppose...Ch. 3 - You ask your neighbor to water a sickly plant...Ch. 3 - Six balls are to be randomly chosen from an urn...Ch. 3 - A type C battery is in working condition with...Ch. 3 - Prob. 3.12STPECh. 3 - Balls are randomly removed from an urn that...Ch. 3 - A coin having probability .8 of landing on heads...Ch. 3 - In a certain species of rats, black dominates over...Ch. 3 - a. In Problem 3.70b, find the probability that a...Ch. 3 - For the k-out-of-n system described in Problem...Ch. 3 - Prob. 3.18STPECh. 3 - Prob. 3.19STPECh. 3 - Suppose that there are n possible outcomes of a...Ch. 3 - If A flips vand B flips n fair coins, show that...Ch. 3 - Prove or give counterexamples to the following...Ch. 3 - Let A and B be events having positive probability....Ch. 3 - Rank the following from most likely to least...Ch. 3 - Two local factories, A and B, produce radios. Each...Ch. 3 - Show that if P(AB)=1, then P(BCAC)=1Ch. 3 - Prob. 3.27STPECh. 3 - A total of 2n cards, of which 2 are aces, are to...Ch. 3 - There are n distinct types of coupons, and each...Ch. 3 - Show that for any events E and F,P(EEF)P(EF) Hint:...Ch. 3 - There is a 60 percent chance that event A will...
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
- Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?arrow_forwardSmokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one pack or less per day. During any month, there is a 5 probability that a nonsmoker will begin smoking a pack or less per day, and a 2 probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10 probability of quitting and a 10 probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5 probability of quitting and a 10 probability of dropping to a pack or less per day. How many people will be in each group a in 1 month, b in 2 months, and c in 1 year?arrow_forwardDividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an 8,000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning and that of B winning if the game were to continue? The French Mathematician Pascal and Fermat corresponded about this problem, and both came to the same correct calculations though by very different reasonings. Their friend Roberval disagreed with both of them. He argued that player A has probability 34 of winning, because the game can end in the four ways H, TH, TTH, TTT and in three of these, A wins. Robervals reasoning was wrong. a Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform the experiment 80 or more times, and estimate the probability that player A wins. bCalculate the probability that player A wins. Compare with your estimate from part a.arrow_forward
Recommended textbooks for you
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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