Question

Suppose a test for cancer is given. If a person has cancer, the test will detect it in 96% of the cases; if the person does not have cancer, the test will show a positive result 1% of the time. If we assume that 12% of the population taking the test actually has cancer, what is the probability (rounded to the nearest percent) that a person taking the test and obtaining a positive actually has cancer?

Answer #1

"To diagnose colorectal cancer, the hemoccult test is
conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who
participate in
screening using the hemoccult test, the following information is
available.
The probability that one of these people has colorectal cancer is
0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he
will have a
positive hemoccult test. If a person does not have colorectal
cancer, the
probability is 3...

Consider a laboratory test to detect a disease.
Let A = {event that the tested person has the disease}
B = {event that the test result is positive}
and it is known that P(B|A) = 0.99, P(B|Ac ) = 0.005, and 0.1
percent of the population actually has the disease.
What is the probability that a person has the disease given that
a test is positive?
a. Work the problem analytically.
b. Write a MATLAB simulator to verify your answer.

"To diagnose colorectal cancer, the hemoccult test is
conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who
participate in
screening using the hemoccult test, the following information is
available.
The probability that one of these people has colorectal cancer is
0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he
will have a
positive hemoccult test. If a person does not have colorectal
cancer, the
probability is 3...

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...

Suppose 1% of a given population have a certain genetic defect.
For a new gene test, it gives a positive result with 90%
probability when an individual does have the genetic defect, and it
gives a positive result with 9.6% probability when an individual
does NOT have the genetic defect.
a. If a person gets a positive
test result, what is the probability that he/she actually has the
genetic defect?
If a person gets a negative test result, what 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 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 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...

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 new, simple test has been developed to detect a particular
type of cancer. The test must be evaluated before it is put into
use. A medical researcher selects a random sample of 2,000 adults
and finds (by othermeans) that 3% have this type of cancer. Each
of the 2,000 adults is given the test, and it is found that the
test indicates cancer in 97% of those who have it and in 1% of
those who do not.
Based...

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