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1)Given P (A) = 0.25 and P (AU B)= 0.50. What must P (B) be if A and B are to be independent?

1)Given P (A) = 0.25 and P (AU B)= 0.50. What must P (B) be if A and B are to be independent?

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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1)Given P (A) = 0.25 and P (AU B)= 0.50. What must P (B) be if A and B are to be independent? 2)In all medical tests, one can experience false negative and false positive results. Et false negative result means that the test says that the person being tested is healthy, while he is in fact ill. A false positive result means that the test says that the person is sick, while the person is actually healthy. Usually the complementary ones are stated the probabilities of these. They are called the sensitivity and specificity of the test. Assume that there has been a new test for the coronavirus SARS-CoV-2, je the virus that causes covid-19. The sensitivity of this test is 85%. This is the probability that the test is positive given that the person being tested is really sick. This event is the complementary to what we call false negative, je that the test is negative given that the test person is actually ill. The specificity of the test is set to 99%. This is the probability that the test is negative given that the patient does not have covid-19. This event is the complementary to what we call false positive, ie that the test is positive given that the test person is not ill. A school must test all students with this test. Assume that 2% of the school's students are covid-19- sick at the time the test is performed. One person is being tested for covid-19 with this new test. a) What is the probability that the test indicates that the person has covid-19? b) The test indicates that the person has covid-19. What then is the probability of that he actually has covid-19?
Transcribed Image Text:1)Given P (A) = 0.25 and P (AU B)= 0.50. What must P (B) be if A and B are to be independent? 2)In all medical tests, one can experience false negative and false positive results. Et false negative result means that the test says that the person being tested is healthy, while he is in fact ill. A false positive result means that the test says that the person is sick, while the person is actually healthy. Usually the complementary ones are stated the probabilities of these. They are called the sensitivity and specificity of the test. Assume that there has been a new test for the coronavirus SARS-CoV-2, je the virus that causes covid-19. The sensitivity of this test is 85%. This is the probability that the test is positive given that the person being tested is really sick. This event is the complementary to what we call false negative, je that the test is negative given that the test person is actually ill. The specificity of the test is set to 99%. This is the probability that the test is negative given that the patient does not have covid-19. This event is the complementary to what we call false positive, ie that the test is positive given that the test person is not ill. A school must test all students with this test. Assume that 2% of the school's students are covid-19- sick at the time the test is performed. One person is being tested for covid-19 with this new test. a) What is the probability that the test indicates that the person has covid-19? b) The test indicates that the person has covid-19. What then is the probability of that he actually has covid-19?
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