A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i.e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i.e., incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i.e., negative) result, what is the probability that she has the disease? Select one: O a. 0.9917 b. 0.00786 O c. 0.215 O d. 0.0358

A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i.e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i.e., incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i.e., negative) result, what is the probability that she has the disease? Select one: O a. 0.9917 b. 0.00786 O c. 0.215 O d. 0.0358

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

Suppose that the rats on the campus of Hypothetical U are found to be carriers of bubonic plague. Eradicating the rats has an estimated cost of $1,000,000 and is expected to reduce the probability a given student dies of the plague from 1/3,000 to zero. Suppose that there are 30,000 students on campus. Suppose further that the administration refuses to eradicate the rats due to the cost. From this information, we can estimate that the administration's willingness to pay to save a student statistical life is no more than $100,000 $1,000,000 $50,000 $33,333
A test to determine whether a certain antibody is present is 99.4% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.4% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.006. Suppose the test is given to seven randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all seven people? (b) What is the probability that the test comes back positive for at least one of the seven people?
If you play roulettes and bet on 'red' the probability that you win is 18/38 = .4737. People often repeat this between several times. We can consider each time we play a 'trial' and consider it a success when we win, so p = 18/38 or (.4737) and q = 20/38 or (.5263). Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays. -when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000. c) what is the mean or expected value of p? d) what is the standard deviation of p? e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places
The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.77, given that a person has tuberculosis. The probability is 0.09 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will fall in the following categories? (Enter your answers to four decimal places.) have tuberculosis and have a positive testnot have tuberculosisnot have tuberculosis and have a positive test
1. A test to determine whether a certain antibody is present is 99.2% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.2% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.008. Suppose the test is given to five randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all five people? (b) What is the probability that the test comes back positive for at least one of the five people? (a) P(all 5 tests are negative) = (Round to four decimal places as needed.) %3D (b) P(at least one positive): (Round to four decimal places as needed.)
Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 95 % . A person who actually has the disease is tested for it using this procedure by two independent laboratories. (1) What is the probability that both test results will be positive? (ii) What is the probability that at least one of the two test results willI be positive?
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 test to determine whether a certain antibody is present is 99.2% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.2% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.008. Suppose the test is given to six randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all six people? (b) What is the probability that the test comes back positive for at least one of the six people?
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.
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?
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)
A disease affects 1 out of 10,000 people. There is a test to check whether a person has the disease. The test is accurate. In particular, we know the following: (a) The probability that the test result is positive given that the person does not have the disease, is only 2 percent. (b) The probability that the test result is negative given that the person has the disease, is only 1 percent. Question: A random person gets tested for the disease and the result comes back positive. What is the probability that the person has the disease?