Question

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 using the theorem.

b. Now, create a contingency table for this problem (your preference):

Answer #1

A certain virus infects one in every 300 300 people. A test used
to detect the virus in a person is positive 90 90% of the time
when the person has the virus and 10 10% of the time when the
person does not have the virus. (This 10 10% 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...

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...

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...

The probability of a randomly selected adult in one country
being infected with a certain virus is 0.005. In tests for the
virus, blood samples from 17 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.
The probability that the combined sample will test positive is
_____.

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 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...

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.

The probability of a randomly selected adult in one country
being infected with a certain virus is 0.003. In tests for the
virus, blood samples from 11 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.

The probability of a randomly selected adult in one country
being infected with a certain virus is 0.006 In tests for
thevirus, blood samples from 27 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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