QUESTION 1A screening test for cancer has a low false positive rateand a low false negative rate, in that, with careful use,one finds the disease in 95% of the patients having it,and only 5% of the patients not having it. Assume that4% of a certain population has the disease. What is a theprobability that a person who reacts positively to the testwill, in fact, have the disease?

Answered: Image /qna-images/answer/5f8285ae-1d62-4ff4-8780-677863973634.jpg

Answered: A screening test for cancer has a low…

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 long-term study revealed that 94% of the men for whom a test was negative do not have cancer. If a man selected at random tests negative for cancer with this test, what is the probability that he does have cancer?
The drop out rate of female students from computer science programs in their first year is much higher compared to males. There are many initiatives that aim to help lower the rate of drop out for females which is currently 0.30. If 310 female students enrolled in the computer science program this year, what is the probability that less than 80 will actually drop out? O A. 0.579 O B. 0.054 O C. 0.421 O D. 0.946 Reset Selection
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
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?
Bryan is performing data entry for an insurance company by taking handwritten records and entering them into the database. Thus far, 15.6% of the handwritten records have had missing data that prevented them from being entered into the database. If Bryan takes 10 handwritten records, what is the probability that at most three records will be incomplete?
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?
1% of all products in a factory are defective. During quality control, a test is applied that detects a defective product with a probability of 0.99, and in 1% of cases it incorrectly rejects a correct product. Find the probability that the product that is rejected is actually correct, as well as the probability that the product that is accepted in the test as correct is in fact defective.
Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false positive in 4% of the cases where the disease is not present. What is the probability that the disease is absent if the test result is negative?
A pharmaceutical company is running trials on a new test for anabolic steroids. The company uses the test on 400 athletes known to be using steroids and 200 athletes known not to be using steroids. Of those using steroids, the new test is positive for 375 and negative for 25. Of those not using steroids, the test is positive for 25 and negative for 175. What is the relative frequency of a false negative result (the probability that an athlete using steroids will test negative)? (Round your answer to two decimal places.) What is the relative frequency of a false positive result (the probability that an athlete not using steroids will test positive)? (Round your answer to two decimal places.)
A drug test facility uses a test that has a 1% false negative rate, and a 2% false positive rate. It is estimated that 4% of the population is taking this drug. If a random person who tested positive is chosen, what is the probability that they are actually taking the drug?
Empirical evidence suggests that 25% of Florida drivers are uninsured. If four random Florida drivers are involved in an accident, what is the probability that more than one of them are uninsured?

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