Only 1 in 1000 adults is afflicted with a rare disease for which a diagnostic test has been developed.The test is such that when an individual actually has the disease, a positive result will occur 99% of thetime, whereas an individual without the disease will show a positive test result only 2% of time. If arandomly selected individual is tested and the result is positive, what is the probability that theindividual has the disease.

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Answered: Only 1 in 1000 adults is afflicted with…

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 genetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. It is believed that 3% of people actually have this predisposition. The genetic test is 98% accurate if a person actually has the predisposition, meaning that the probability of a positive test result when a person actually has the predisposition is 0.98. The test is 97% accurate if a person does not have the predisposition. What is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition? (Round your answer to four decimal places.)
An observer stands at a highway overpass and counts the automobiles that pass by. When he sees a red automobile, he stops counting. What is the likelihood that 10 automobiles will be spotted if the probability of red cars is 0.20?
A diagnostic test for disease X correctly identifies the disease 95% of the time. False positives occur 7%. It is estimated that 5.13% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. What is the percentage chance that, given a negative result, the person does not have disease X? What is the percentage chance that, the person will be misclassified?
Only 6% of people has 0-negative blood type. If a local blood drive has 100 donors, what is the probability that at least 10 of the 100 donors has O-negative blood?
If an affected female XLX marries an unaffected male XY, what is the probability of passing the hypertrichosis gene to her offspring? Remember hypertrichosis is an X-linked dominant disease. If an affected male XLY marries an unaffected female XX, what is the probability of passing the hypertrichosis gene to his offspring?
A diagnostic test for disease X correctly identifies the disease 90% of the time. Flase positives occur 12%. It is estimated that 5.36% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. What is the percentage chance that given a negative result, the person does not have disease X? What is the percentage chance that, the person will be misclassified?
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?
An experiemental drug has been shown to be 75% effective in eliminating symptoms of allergies in animals studies. A small human study involve 6 participants is conducted. What is the probability that the drug is effective on half of the participants
Apparently, depression significantly increases the risk of developing dementia later in lift (BBC News, July 6, 2010). In a recent study it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression. What is the probability of a person developing dementia? If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?
A drug manufacturer claims that their drug cures a certain blood disease 78% of the time. To check the claim, BFAD used the drug in a clinical trial of 100 individuals inflicted with the disease and decided to accept the claim if 70 or more are cured. What is the probability that the claim will be accepted when the cure probability is as low as 0.6?
Assume that a student alarm clock has a 6.6 % daily failure rate. What is the probability that the students alarm clock ill not work on the day of an important final exam?
Assume a students alarm clark has a 13.4% daily failure rate, what is the probability that 2 alarm clocks will fail on the morning of an important final exam

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