One percent of women at age forty who participate in routine screening have brea
ID: 3249001 • Letter: O
Question
One percent of women at age forty who participate in routine screening have breast cancer (prevalence). Eighty percent of women with breast cancer will get positive mammographies (sensitivity). Finally, 9.6% of women without breast cancer will also get positive mammographies (false positives).
(a) In a population of 100,000 women aged forty, how many would be expected to get positive mammographies?
(b) A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
please show all steps and equations used
Explanation / Answer
No of women who have breast cancer = 1%
Total percentage of women who have breast cancer and will get positive mammographies =
80% of total women who have breast cancer i.e. 80% of 1% = 0.8%
Women who dont have breast cancer =99% of total women aged 40
women who get false positives = 9.6% of 99% = 9.504% total
a) Total Population = 100000
Positive Mammographies = Sensitivity + False Positives
= (0.8% of 100000)+(9.504% of 100000)
=800+9504
=10304
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b)False positive cases = 9504
Actual breast cancer with positive mammographies = 800
Total Cases = 10304
Probability of her actually having a breast cancer =Choosing one out of true cases /Total Cases
= 800C1 / 10304C1
=0.07764
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