EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
Author: Ross
Publisher: VST
expand_more
expand_more
format_list_bulleted
Question
Chapter 3, Problem 3.79P
To determine
To show: That the
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Patterns in Floor Tiling A square floor is to be tiled with square tiles as shown. There are blue tiles on the main diagonals and red tiles everywhere else.
In all cases, both blue and red tiles must be used. and the two diagonals must have a common blue tile at the center of the floor.
If 81 blue tiles will be used, how many red tiles will be needed?
For what numbers in place of 81 would this problem still be solvable?
Find an expression in k giving the number of red tiles required in general.
At a BBQ, you can choose to eat a burger, hotdog or pizza. you can choose to drink water, juice or pop. If you choose your meal at random, what is the probability that you will choose juice and a hot dog? What is the probability that you will not choose a burger and choose either water or pop?
a card is drawn from a standard deck of 52 cards. If a card is choosen at random, what is the probability that the card is a)heart b)a face card or c)a spade or 10
Chapter 3 Solutions
EBK FIRST COURSE IN PROBABILITY, A
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 - Suppose distinct values are written on each of 3...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 - Twenty percent of Bs phone calls are with her...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 - There is a 30 percent chance that A can fix her...Ch. 3 - In any given year, a male automobile policyholder...Ch. 3 - An urn contains 5 white and 10 black balls. A fair...Ch. 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 - Players A, B, C, D are randomly lined up. The...Ch. 3 - Players 1,2,3 are playing a tournament. Two of...Ch. 3 - Suppose there are two coins, with coin 1 landing...Ch. 3 - In a 7 game series played with two teams, the...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 - 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 - 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. 3.79PCh. 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 an eight team tournament with the format...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 - Each of n workers is independently qualified to do...Ch. 3 - Suppose in the preceding problem that n=2 and that...Ch. 3 - Each member of a population of size n is,...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 - Independent trials that result in a success with...Ch. 3 - Suppose that n independent trials are performed,...Ch. 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 - Suppose that a nonmathematical, but...Ch. 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 - a. If the odds of A is 23, what is the probability...Ch. 3 - Prob. 3.32STPECh. 3 - If the events E, F, G are independent. show that...Ch. 3 - Players 1,2,3, are in a contest. Two of them are...Ch. 3 - If 4 balls are randomly chosen from an urn...Ch. 3 - In a 4 player tournament, player 1 plays player 2,...Ch. 3 - In a tournament Involving players 1,..., n,...
Knowledge Booster
Similar questions
- in a coffee shop, 160 customers came in. Of these, 60 bought coffe and cake and the rest ordered just coffee. determine the probability that the next person will buy coffee and cakearrow_forwardTwo dice are rolled and their sum calculated. Draw a table to show all of the possibilities. Determine the theoretical probability of rolling a sum of 7. And determine the theoretical probability of rolling a sum greater than 9arrow_forwardA football player makes 350 out of every 400 passes he throws. In a game he usually throws 26 passes. Estimate how many of these passes will be successfularrow_forward
- Q prove or disprove: If Ely/x) = x = c(dipy =BCCo (BVC) ECxly)=y, and E(X2), Ely)arrow_forwardIn a small office, there are m = 5 typists who need to use a single typewriter to complete their reports. Assume the time each typist takes to prepare a report follows an exponential distribution with an average of 20 minutes per preparation (A = 3 reports/hour), and the service time for the typewriter to type out a report also follows an exponential distribution, averaging 30 minutes to complete a report (μ 2 reports/hour). Given that the number of typists is finite and all typists = share one typewriter, they will form a waiting queue. (1). Describe this queuing system and explain how it fits the characteristics of the M/M/1/∞0/m model. (2). Calculate the probability that any typist is using the typewriter at steady-state. (3). Calculate the average number of typists waiting in the queue at steady-state. (4). Considering the need to reduce waiting time, if an additional typewriter is introduced (turning into a two-server system, or M/M/2/∞0/m model), analyze the expected impact,…arrow_forwardCan you tell the answerarrow_forwardTheorem 2.4 (The Hölder inequality) Let p+q=1. If E|X|P < ∞ and E|Y| < ∞, then . EXY SEXY ≤ Xp Yq.arrow_forward2 P(x,y). kx²y X: 1,2 5.11273 Find k Find P(x/y) ③ Mxy Ng q oxy วarrow_forwardThe joint density function of two continuous random variables X and Y is: p(x, y) = {Kcos(x + y) Find (i) the constant K 0 0arrow_forwardp(x,y) = {e-x -(x+y) 0 x ≥ 0, y ≥ 0 otherwise find x,y,Exy, by Охarrow_forwardIf X is a continuous random variable having pdf as shown. Find a) the constant k b) P(X>1) c) X, X², 0%, standard deviation. n(x) k -2 -1 0 1 2arrow_forwardThe joint probability function for the random variables X and Y is y 0 1 2 P(X, Y) = x0 [3/28 9/28 3/281 = 13/14 3/14 2 1/28 0 0 0 Find Mx, My, E(XY), OXY.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning