Question

A certain virus infects one in every 200 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 the probability that the person is infected.

(b) Using Bayes' Theorem, when a person tests negative, determine the probability that the person is not infected.

Answer #1

A certain virus infects one in every
200200
people. A test used to detect the virus in a person is
positive
9090%
of the time when the person has the virus and
1010%
of the time when the person does not have the virus. (This
1010%
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 200 people. A test used to
detect the virus in a person is positive 85% 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 200 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 is infected" and B be the event "the person
tests positive". Hint: Make a Tree Diagram a) Find the probability
that...

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 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 2000 people. a test used to
detect the virus in a person is positive 96% of the time if the
person has the virus and 4% of the time if the person does not have
the virus. Let A be the event "that the person is infected" and B
be the event "the person tests positive."Find the probability that
a person does not have the virus given that they test negative,
i.e. find...

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...

3. The flu virus infects 1 in every 250 people. The test
used to detect the flu shows a positive result 70% of the time when
the person actually has the flu and shows a positive result 15% of
the time when a person does not have the flu. Event A will be a
“person who is infected”. Event B will be a “person who tests
positive.” Hint: Use a tree diagram.
(a) Given that a person tests positive, what...

A certain virus infects 5% of the population. A test used to
detect the virus in a person is positive 80% of the time if the
person has the virus, and 10% of the time if the person does not
have the virus.
a. What is the probability that a randomly selected person
tested positive and has the virus?
b. What is the probability that a randomly selected person
tested positive and does not have the virus?
c. What is...

Problem 9: Suppose the probability of being infected with a
certain virus is 0.005. A test used to detect the virus is positive
90% of the time given that the person tested has the virus, and
positive 5% of the time given that the person tested does not have
the virus. (2 points)
a. Use Bayes’ Theorem to find the probability that a person has
the virus, given that they tested positive. Clearly show your work
and how you are...

The probability of a randomly selected adult in one country
being infected with a certain virus is 0.004. In tests for the?
virus, blood samples from 25 people are combined. What is the
probability that the combined sample tests positive for the? virus?
Is it unlikely for such a combined sample to test? positive? Note
that the combined sample tests positive if at least one person has
the virus.

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