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 mammogram is positive, what is the probability that she has breast cancer?
c) Interpret your answer for P(C | +).
4.
(a)
It is given that,
From the given data,
1.5% of women have breast cancer.
92% of women having breast cancer tests positive.
9% of women have false positive mammograms i.e. 9% of women not having breast cancer tests positive.
(b)
The event that a randomly selected woman has breast cancer given that her mammogram is positive is denoted as (C|+).
Using Bayes' theorem we have,
(c)
The value of P(C|+) interprets that 13.47% of women who are tested positive in mammogram have breast cancer.
Get Answers For Free
Most questions answered within 1 hours.