7. There is a test for allergy to people, but this test is not always right:
For people that really do have the allergy, the test says "yes" 80% of the time
For people that do not have the allergy, the test says "yes" 10% of the time ("false positive")
If 1% of the population have the allergy,
a) what is the probability that the test says "yes"?
b) given the test says "yes" what are the chances that a person really has the allergy?
7. There is a test for allergy to people, but this test is not always right:...
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". a) Find the probability that a person has the virus...
Assume that 0.1% of people from a certain population have a germ. A test gives false positive in 10% of cases when the person does not have this germ. This test gives false negative in 20% of cases when this person has this germ. Suppose you pick a random person from the population and apply this test twice. Both time it gives you positive result. What is the probability that this person actually has this germ?
Over for bonus question® 2. (+10) The reliability of a particular test for the Ebola virus is as follows: If the subject has Ebola, the test comes back positive of the time. If the subject does not have Ebola, the test res back positive 1% of the time. From a large population, in which 2 in every 10,000 people have Ebola, a person is selected at random and given the test, which comes back positive. SHOW ALL WORK AND CIRCLE...
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80% of the time when the person has the virus and 15 % of the time when the person does not have the virus. (This 15 % result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive." (a) Using Bayes' Theorem, when a person tests...
A certain virus infects one in every 250 people. A test used to detect the virus in a person is positive 80% of the time when the person has the virus and 15% of the time when the person does not have the virus. (This 15% result is called a false positive) Let A be the event "the person is infected" and B be the event "the person tests positive." (a) Using Bayes' Theorem, when a person tests positive, determine...
A screening test for a rare form of TB has a 7% false positive rate (i.e. indicates the presence of the disease in people who do not have it). The test has an 8% false negative rate (i.e. indicates the absence of the disease in people who do have it). In a population of which 0.6% have the disease, what is the probability that someone who tests positive has the disease?
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% of the time when the person has the virus and 15% of the time when the person does not have the virus. (This 15% result is called a false positive.) Let A be the event the person is infected" and B be the event the person tests positive." (a) Using Bayes' Theorem, when a person tests positive, determine...
A certain virus infects one in every 500 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the person is infected" and B be the event "the person tests positive." (a) Find the probability that a person has the virus given that they have tested positive. (b)...
A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". a) Find the probability that a person has the virus...
It is estimated that 1% of all people have a particular disease. The test for this disease has a false positive rate of 2%, and a false negative rate of 3%. 1. Draw a tree diagram for this experiment. 2. Suppose that a person is selected at random and tested. Given that the test is negative, what is probability that the person does not have the disease?