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(a) Find the probability that the test result for a randomly selected person is positive. (b) If the test result is positive, what is the probability that the person has COVID19? (e) If the test result is negative, what is the probability that the person has COVID19? This is known as the post-test probability of infection. (d) Suppose a person tests negatively twice (and the tests are assumed independent), what is the probability that the person has COVID19?

(a) Find the probability that the test result for a randomly selected person is positive. (b) If the test result is positive, what is the probability that the person has COVID19? (e) If the test result is negative, what is the probability that the person has COVID19? This is known as the post-test probability of infection. (d) Suppose a person tests negatively twice (and the tests are assumed independent), what is the probability that the person has COVID19?

A First Course in Probability (10th Edition)
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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5. You might be wondering: if you have just received a negative test for COVID19, is the probability that you are infected equal to zero? Are you safe to visit your grandparents? There are two measures of the effectiveness of a test for the presence of a disease. The sensitivity of a test (TPR or true positive rate) is the probability that the test is positive given that the person has the disease. The specificity (TNR or true negative rate) is the probability that the test is negative given that the person does not have the disease. A good test would have TPR and TNR values close to one. To define sensitivity and specificity using statistical language, let A be the event "person tests positive" and let B be the event "person has the disease". The sensitivity or TPR would be P(AB) and the specificity or TNR would be P(AB).The nasopharyngeal swab and/or throat swab tests used for COVID19 have sensitivity between 70% and 90% and specificity above 95%. Suppose a Covid test is administered to a subset of a population in which a proportion of the population p has the disease. Assume the values TPR = 0.7, TNR = 0.95 and p = 0.02. For each of the following questions, define the events required for the calculation and find the probability. (a) Find the probability that the test result for a randomly selected person is positive. (b) If the test result is positive, what is the probability that the person has COVID19? (e) If the test result is negative, what is the probability that the person has COVID19? This is known as the post-test probability of infection. (d) Suppose a person tests negatively twice (and the tests are assumed independent), what is the probability that the person has COVID19?
Transcribed Image Text:5. You might be wondering: if you have just received a negative test for COVID19, is the probability that you are infected equal to zero? Are you safe to visit your grandparents? There are two measures of the effectiveness of a test for the presence of a disease. The sensitivity of a test (TPR or true positive rate) is the probability that the test is positive given that the person has the disease. The specificity (TNR or true negative rate) is the probability that the test is negative given that the person does not have the disease. A good test would have TPR and TNR values close to one. To define sensitivity and specificity using statistical language, let A be the event "person tests positive" and let B be the event "person has the disease". The sensitivity or TPR would be P(AB) and the specificity or TNR would be P(AB).The nasopharyngeal swab and/or throat swab tests used for COVID19 have sensitivity between 70% and 90% and specificity above 95%. Suppose a Covid test is administered to a subset of a population in which a proportion of the population p has the disease. Assume the values TPR = 0.7, TNR = 0.95 and p = 0.02. For each of the following questions, define the events required for the calculation and find the probability. (a) Find the probability that the test result for a randomly selected person is positive. (b) If the test result is positive, what is the probability that the person has COVID19? (e) If the test result is negative, what is the probability that the person has COVID19? This is known as the post-test probability of infection. (d) Suppose a person tests negatively twice (and the tests are assumed independent), what is the probability that the person has COVID19?
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