Question

Mammography is used as a form of early detection of breast cancer in women. We know that if a woman has breast cancer, mammography will detect it 90% of the time. If the woman does not have breast cancer, then mammography will give a positive result 7% of the time. We also know that there is a 0.8% chance that any given woman has breast cancer.

What is the probability that a woman has breast cancer if she has a positive mammogram?

Answer #1

Approximately 1% of women aged 40-50 have breast cancer. A woman
with breast cancer has a 90% chance of a positive test from a
mammogram, while a woman without has a 10% chance of a false
positive result. What is the probability a woman has breast cancer
given that she just had a positive test

Suppose a particular woman tests positive; what is the
probability that she has breast cancer?
To pin this question , please consider a population in which 1%
of women have breast cancer, and a mammography test which has a 90%
chance of returning a correct result. That is, if a woman has
cancer then there is a 90% chance the test will be positive, and if
a woman does not have cancer then there is a 90% chance the test...

*8.21 Assume that the probability of breast cancer equals .01
for women in the 50–59 age group. Furthermore, if a woman does have
breast cancer, the probability of a true positive mammogram
(correct detection of breast cancer) equals .80 and the probability
of a false negative mammogram (a miss) equals .20. On the other
hand, if a woman does not have breast cancer, the probability of a
true negative mammogram (correct non detection) equals .90 and the
probability of a...

The following hypothetical scenario concerns a population of
women aged 50 and older. We know that 1% of this population has
breast cancer at this time. The probability of testing positive on
a mammogram is 90% for women who actually do have cancer (true
positive result), and 8% for women who do not have it (false
positive result). (a) Find the proportion of all negative mammogram
results for this population. (8 points) (b) Given that a randomly
selected woman has...

Part 4: Probability
In this part, you will work with probabilities.
1) Consider rolling two four sided dice. One die is blue and the
other is green.
(a) State the sample space.
(b) Compute the probability of getting two even numbers.
(c) Compute the probability of getting an even sum if the blue
die rolls a 2.
2) What is the probability of drawing a four or a heart when
drawing a single card from a standard
deck of cards....

Question 4: A-E parts
A) Consider rolling two four sided dice. One die is blue
and the other is green.
(1) State the sample space.
(2) Compute the probability of getting two even
numbers.
(3) Compute the probability of getting an even sum if
the blue die rolls a 2.
B)
(1)What is the probability of drawing a four or a heart
when drawing a single card from a standard deck of
cards?
C) Consider a machine that fills 275...

80. Of women who undergo regular mammograms, two percent
have breast cancer. If a woman has breast cancer, there is a 90%
chance that her mammogram will come back positive. If she does not
have breast cancer there is a 10% chance that her mammogram will
come back positive. Given that a woman’s mammogram has come back
positive, what is the probability that she has breast
cancer?
81. The Triangle is a neighborhood that once housed a
chemical plant but...

4. One and a half percent (1.5%) of women over 55 have breast
cancer. Ninety-two percent (92%) of all women who have breast
cancer test positive on mammograms. Nine percent (9%) of women will
have false positive mammograms. Define the events: C: {a woman has
breast cancer} and +: {the mammogram is positive}.
a) Write down what is given in the problem, both explicitly and
implicitly, using the events defined in the problem
description.
b) If a randomly selected woman’s...

Mammograms are a relatively inexpensive and nonintrusive way to
test for breast cancer. Suppose that mammogram screenings are 93%
specific and 87% sensitive. This means that those without breast
cancer test negative 93% of the time and those with breast cancer
test positive 87% of the time. Answer the following questions as if
12.6% of all women have breast cancer.
a) Given that a women tests negative, what is the probability
that she has breast cancer?
(b) Given that a...

Cancer Screening ~ Breast cancer is the most
common cancer in females in the United States and throughout the
world. Digital mammography test (the process of using low-energy
X-rays to examine the human breast for diagnosis and screening) is
one of the typical techniques for early detection of breast cancer
in recent years. According to a study, digital mammography test has
a sensitivity of 0.97, and a specificity of 0.63 for breast cancer
detection.
Round all numeric answers to four...

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