When a message that is communicated via public communication networks is received, it must be authenticated. This is done by using a secret enciphering key. Even though the key is secret, there is always the possibility that it will fall into the wrong hands, thus allowing an unauthentic message to appear to be authentic. Assume that 95% of all messages received are authentic. Furthermore, assume that only 0.1% of all unauthentic messages are sent using the correct key and that all authentic messages are sent using the correct key. Find the probability that a message is authentic given that the correct key is used.

When a message that is communicated via public communication networks is received, it must be authenticated. This is done by using a secret enciphering key. Even though the key is secret, there is always the possibility that it will fall into the wrong hands, thus allowing an unauthentic message to appear to be authentic. Assume that 95% of all messages received are authentic. Furthermore, assume that only 0.1% of all unauthentic messages are sent using the correct key and that all authentic messages are sent using the correct key. Find the probability that a message is authentic given that the correct key is used.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

John Allen Paulos has pointed out a problem with massive, untargeted wiretaps. To illustrate the problem, he sup-poses that one out of every million Americans has terrorist ties. Furthermore, he supposes that the terrorist profile is 99% accu-rate, so that if a person has terrorist ties, the profile will pick them up 99% of the time, and if the person does not have ter-rorist ties, the profile will accidentally pick them up only 1% of the time. Given that the profile has picked up a person, what is the probability that the person actually has terrorist ties? Dis-cuss how your answer affects your opinion on domestic wire-tapping. Source: Who’s Counting.
suppose that from a sample of 200,000 new york workers, 32,400 reported traveling more than an hour an day. From this information, statisticians determined that about 16.2% of the workers in the state traveled more than an hou to work every day in 2011. If there were 8,437,512 workers in the entire population, about how many traveled more than an hour to work each day?
The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on - time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse A are Southwest Airlines flights, 35% are US Airways flights, and 25% are JetBlue flights. An announcement has just been made that Flight 1424 will be arriving at gate 20 in concourse A. What is the most likely airline for this arrival? What is the probability that Flight 1424 will arrive on time? Suppose that an announcement is made saying that Flight 1424 will be arriving late. What is the most likely airline for this arrival? What is the least likely airline? Develop a joint probability table with three rows (airlines) and two columns (on-time arrivals vs. late arrivals). What is the highest probability…
In 1940, a county land-use survey showed that 10% of the county land was urban, 50% was unused, and 40% was agricultural. Five years later, a follow-up survey revealed that 70% of the urban land had remained urban, 10% had become unused, and 20% had become agricultural. Likewise, 20% of the unused land had become urban, 60% had remained unused, and 20% had become agricultural. Finally, the 1945 survey showed that 20% of the agricultural land had become unused while 80% remained agricultural. Assuming that the trends indicated by the 1945 survey continue, compute the percentages of urban, unused, and agricultural land in the county in 1950 and the corresponding eventual percentages.
The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on - time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse A are Southwest Airlines flights, 35% are US Airways flights, and 25% are JetBlue flights a)Suppose that an announcement is made saying that Flight 1424 will be arriving late. What is the most likely airline for this arrival? What is the least likely airline? b)Develop a joint probability table with three rows (airlines) and two columns (on-time arrivals vs. late arrivals). What is the highest probability and the lowest? c)An announcement has just been made that Flight 1424 will be arriving at gate 20 in concourse A. What is the most likely airline for this arrival? d)What is the probability that Flight…
The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse Aare Southwest Airlines flights, 35% are US Airways flights, and 25% are jetBlue flights. a) Deveiop a joint probability table with three rows (airlines) and two
Suppose that 32 students signed up for classes during an orientation session. If exactly 20 of them signed up for chemistry and exactly 16 of them signed up for English, how many of them signed up for both chemistry and english? apply Polya's four step strategy
Suppose that 60% of all students who have to buy a text for a particular course want a new copy, whereas the others want a used copy. Consider randomly selecting 15 purchasers, is a result of 12 a significantly high value for people who want a used copy of the book?
2. A research Development department at Oda manufacturing company determines that 20% of people who purchase their products during any given month will not purchase the next month. On the other hand, 30% of the people-who could not purchase during any given month will purchase in the next month. On a population of 1000 people 100 purchased their products this month. How many will purchase their product. A. In the long run?
An analysis of first-year students at a college revealed that 1/5 of the first-year women were from homes where both parents were professionals. Of these, 3/4 were interested in the same profession as one or both of their parents. If this latter group is made up of 15 students, how many first-year women are there?
Kentville, a community of 10,000 people, resides next to a krypton mine, and there is a concern that the emission from the krypton smelter have resulted in adverse effects. Specifically, Kryptonosis seems to have killed 12 of Kentville’s inhabitants last year. A neighboring community, Lanesburg, has 25,000 inhabitants and is far enough from the smelter to not be affected by the emission. In Lanesburg, only three people last year died of Kryptonosis. Given that the number of deaths in Kentville and their causes last year were: Heart attack=7 Accidents=4 Kryptonosis=12 Other=6 What is the risk of dying of Kryptonosis in Kentville relative to non-contaminated locality?What is the risk of dying of Kryptonosis in Kentville relative to deaths due to other causes? How many times the chance of dying of Kryptonosis compared to dying of accidents ? How many times the chance of dying of Kryptonosis compared to Other causes?
A certain cat shelter has devised a novel way of making prospective adopters choose their new pet. To remove pet owners’ biases regarding breed, age, or looks, they are led blindfolded into a room containing all the cats up for adoption and must bring home whichever they pick up. Suppose you are trying to adopt two cats, and the shelter contains a total of N cats in one of only two colors: black or orange. Is it possible that you will come out of the room with two black cats with a probability of ½? If so, how many cats should be in the room? How many black, how many orange?