Question

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 given that they
have tested positive, i.e. find P(A|B). Round your answer to the
nearest tenth of a percent and do not include a percent sign.

P(A|B)= %

b) Find the probability that a person does not have the virus given
that they test negative, i.e. find P(A'|B'). Round your answer to
the nearest tenth of a percent and do not include a percent
sign.

P(A'|B') = %

Answer #1

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 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 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 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
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 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...

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...

11. Virus:
In a city with a population of 10,000, 100 are infected with a
novel virus; the other 9,900 are not.
The government has moved quickly to develop a test that is
meant to detect whether the virus is present, but it is not
perfect:
If a person genuinely has the virus, it is able to properly
detect its presence 96% of the time.
If a person genuinely does not have the virus, the test will
mistakenly conclude its...

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