Question

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 that a randomly selected person has the virus given that they get a positive test result?

Show which rule you use to calculate the probability!

Answer #1

D+→having virus.(inflected?

D-→not having virus(not inflected)

T+→test is positive

P(D+)= 5%=0.05

P(D-)= 0.95

P(T+/D+)= 80%=0.80

P(T+/D-)= 0.10

Now we have to find

a)

the probability that a randomly selected person tested positive and has the virus

=P(T+/D+)

=0.80

b)

the probability that a randomly selected person tested positive and does not have the virus

= P(T+/D-)

= 0.10

C)#using bays theorem:

the probability that a randomly selected person has the virus given that they get a positive test result

P(D+/T+)

= [P(D+)*P(T+/D+)]÷[P(D+)*P((T+/D+)+P(D-)*P(T+/D-)]

=(0.05*0.80)/(0.05*0.80+0.95*0.10)

=0.296296

Thanks!

Stay safe!

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 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 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 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 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
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...

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...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 11 minutes ago

asked 15 minutes ago

asked 31 minutes ago

asked 31 minutes ago

asked 31 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 46 minutes ago

asked 52 minutes ago

asked 54 minutes ago

asked 59 minutes ago