EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3, Problem 3.72P
In Problem 3.70a, find the conditional
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A spacecraft navigation system consists of components of two types - A and B - connected in
a series-parallel arrangement, as in Figure 1.2.
A
B
A
B
B
Figure 1.2 Illustration of series-parallel system
The system will function as long as at least one component of each type functions. The
probability that a type A component will function correctly throughout the planned lifetime of
the spacecraft is 0-9; the corresponding probability for a component of type B is 0-8.
Components may be assumed to fail independently of one another.
The numbers of components of the two types may be varied in order to adjust the probability
of failure of the navigation system.
(a) Show that a requirement that the probability of failure of the entire system should be less
than 1% may be met by using three components of each type (as in the diagram above).
(b) If components of type A weigh 1 kg, while those of type B weigh 2 kg, what is the
composition of the most reliable navigation system weighing 11 kg or…
A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.92, and the probability that both components do so is 0.85. Given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also?
A spacecraft navigation system consists of components of two types - A and B connected in
a series-parallel arrangement, as in Figure 1.2.
A
B
A
B
A
B
Figure 1.2 Illustration of series-parallel system
The system will function as long as at least one component of each type functions. The
probability that a type A component will function correctly throughout the planned lifetime of
the spacecraft is 0.9; the corresponding probability for a component of type B is 0.8.
Components may be assumed to fail independently of one another.
The numbers of components of the two types may be varied in order to adjust the probability
of failure of the navigation system.
(a) Show that a requirement that the probability of failure of the entire system should be less
than 1% may be met by using three components of each type (as in the diagram above).
(b) If components of type A weigh 1kg, while those of type B weigh 2 kg, what is the
composition of the most reliable navigation system weighing 11 kg or…
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
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
- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardI'm mainly struggling to understand part Carrow_forwardConsider an M/M/1 queueing system. If λ = 6 per hour and μ = 8 per hour find the probability of at least 10 customers in the system.arrow_forward
- 8.arrow_forwardA piece of equipment will function only when the three components A, B and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will fail before the end of the year?arrow_forwardIn a M/M/1 model, the service rate is 35 per hour, and arrival rate is 14 per hour. Then, the probability that the system contains exactly one customer isarrow_forward
- Question 1. The apparatuses of a “6-component system” are to be randomly chosen from a box of 20 used apparatuses. The resulting system will be functional if at least 4 of its 6 apparatuses are in working circumstances. If 5 of the 20 components in the box are not in working circumstances, what is the probability that the resulting system will be a nonfunctional ?arrow_forwardWhat is the probability that the current goes from a to b? Each component is independent and the probability that it works is shown in each one. Note: P (A∪B) = 1 − P [(A∪B) ′] = 1 − P (A′∩B ′) Select one:to. 0.898b. 0.998c. 0.102d. 0.812arrow_forward(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) orarrow_forward
- EXAMPLE 6.67 If λ = 2 per hour and = 3 per hour in an M/M/4/N queueing system and there are 2 chairs for waiting customers, calculate the probability that there are 7 customers in the system.arrow_forwardA system consists of two components. The probability that the second component functions in a satisfactorymanner during its design life is 0.9, the probability that at least one of the two components does so is 0.96,and the probability that both components do so is 0.75. Given that the first component functions ina satisfactory manner throughout its design life, what is the probability that the second one does also?arrow_forwardConstruct a copy of figure 3.16 in your text, where the first outcome is one of X and Y the second outcome is one of A and B if the first outcome is X, and one of A, B, and C if the first outcome is Y. Use the following probabilities instead of those given in your text:Pr[X]=0.7Pr[X]=0.7Pr[Y]=0.3Pr[Y]=0.3Pr[A|X]=0.3Pr[A|X]=0.3Pr[B|X]=0.7Pr[B|X]=0.7Pr[A|Y]=0.5Pr[A|Y]=0.5Pr[B|Y]=0.4Pr[B|Y]=0.4Pr[C|Y]=0.1Pr[C|Y]=0.1 (3) Pr[Y|B]=Pr[Y|B]= (4) Pr[B|Y]=Pr[B|Y]=arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
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