A new medical test has been designed to detect the presence of themysterious Brainlesserian disease. Among those who have the disease, theprobability that the disease will be detected by the new test is 0.74. However, theprobability that the test will erroneously indicate the presence of the disease in thosewho do not actually have it is 0.04. It is estimated that 17 % of the population whotake this test have the disease.If the test administered to an individual is positive, what is the probability that theperson actually has the disease?Answer:

Solution: From the given information,

Answered: A new medical test has been designed to…

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...

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A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.7. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 18% of the population who take the test have the disease. If the test is administered to an individual is positive, what is the probability that the person actually has the disease?
During an episode of tonight show, a talk show host related "The birthday problem " to the audience noting that in a group of 50 or more people, probablists have calculated that the probability of atleast 2 people having the same birthday is very high. To illustrate this point he proceeded to conduct his own experiment. A person selected at random from the audience was asked to state his birthday. The host then adked whether anyone in the audience had the same birthday. The response was negative. He repeated the experiment. Once again the response was negative. These results observed the host,were contrary to expectations. In a later episode of the show, the host explained why the experiment had been improperly conducted. Explain why the host failed to illustrate the point he was trying to make in the earlier episode
A new medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.74. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 14 % of the population who take this test have the disease.If the test administered to an individual is positive, what is the probability that the person actually has the disease?
A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.7% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.003. Suppose the test is given to seven randomly selected people who do not have the antibody. What is the probability that the test comes back negative for all sevenpeople? and what is the probability that the test comes back positive for at least one of the seven people?
The ebola virus has an incidence rate of 15%. If the false negative is 25% and the following false positive is 30%, then find what is the conditionsl probability of an individual not having ebola, given they received a negative test result? a. 0.97 b. 0.91 c. 0.94 d. 0.88
We believe that 95% of the population of all Elementary Statistics students consider Statistics an exciting subject. Suppose we randomly and independently selected 20 students from the population. If the true percentage is really 95% find the probability of observing 19 or more of the students who consider statistics to be an exciting subject in our sample of 20.
A certain virus affects 0.7% of the population. A test used to detect the virus in a person is positive 88% of the time if the person has the virus (true positive) and 13% of the time if the person does not have the virus (false positive) Fill out the remainder of the following table and use it to answer the two questions below based on a total sample of 100,000 people. a. Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest hundredth of a percent and do not include a percent sign. b. Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest hundredth of a percent and do not include a percent sign.
In a new fiber-optic communication system, trans- mission errors occur at the rate of 1.5 per twenty seconds. What is the probability that more than five errors will occur during the next minute?
Words that are more likely to be contained in a phishing scam are called flagged words. Typically, there is a 94% chance that a phishing scam contains flagged words. There is a 20% chance that regular email contains flagged words. A security company estimates that 4.9% of emails are phishing scams. An email just came through that contains a flagged word. What are the chances that it is a phishing scam? (Enter the probability as a decimal rounded to four decimal places.)
A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.75; that is, the probability that it will activate the sprinkler when it should is 0.75. The other type, which operates independently of the first type, has a reliability of 0.85. If either device is triggered, the sprinkler will activate. Suppose a fire starts near a sprinkler head. (provide your answer in four decimal numbers) (i) What is the probability that the sprinkler head will be activated? (1.5) (ii) What is the probability that the sprinkler head will not be activated? (1.5) (iii) What is the probability that both activation devices will work properly? (1.5) (iv) What is the probability that only the device with reliability 0.75 will work properly? (1.5)

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