Question
In: Statistics and Probability
(10pts) A particular test is used to determine if an individual has a certain virus. Amongt...
(10pts) A particular test is used to determine if an individual has a certain virus. Amongt the population being tested, 2% has the virus and 98% does not have the virus. The test will arrive at three possible outcomes: Positive, negative, or inconclusive. The following table of values summarizes the various probabilities of the test outcomes for those with the virus and for those without the virus. outcome of test has the virus does not have the virus Positive test 0.96 0.01 Negative test 0.02 0.94 Inconclusive test 0.02 0.05 For example, amongst those individuals who have the virus, the test will yield a negative result with probability 0.02. With this information, compute the following probabilities. a. Prob(has the virus|the test is inconclusive); b. Prob(does not has the virus|the test is inconclusive); c. Prob(the test is inconclusive).
Solutions
orchestra answered 1 year agoRelated Solutions
A certain virus infects 10 in every 1000 people. A test used to detect the virus...
A certain virus infects 10 in every 1000 people.
A test used to detect the virus in a person is positive 80% of
the time when the person has the virus (20% false negative), and 5%
of the time when the person does not have the virus (5% false
positive).
That is 20% of of the time when the test should be positive but
didn't, and 5% of the time the test indicated positive and
shouldn't.
1) Out of all...
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A certain virus infects 1 in every 600 people. A test used to
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have the virus. Let A be the event that the 'person is infected'
and B be the event that the 'person tests positive'
A: Find the probability that the person has the virus given that
they tested positive
B:...
A certain virus infects one in every 400 people. A test used to detect the virus...
A certain virus infects one in every 400 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) Find...
A certain virus infects one in every 400 people. A test used to detect the virus...
A certain virus infects one in every 400 people. A test used to
detect the virus in a person is positive 80% 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...
A certain virus infects one in every 400 people. A test used to detect the virus...
A certain virus infects one in every 400 people. A test used to
detect the virus in a person is positive 85% 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 has the virus" and B be the event "the person
tests positive".
1) Find the probability that A person has the...
A certain virus infects one in every 150 people. A test used to detect the virus...
A certain virus infects one in every
150
people. A test used to detect the virus in a person is
positive
80%
of the time when the person has the virus and
55%
of the time when the person does not have the virus. (This
55%
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,
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The Covid-19 virus infects 10% of the people in a certain
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