female population is about 12.4%, calculate the probability that a woman actually has breast cancer given that she receives a positive screening result at her first mammogram.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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The accuracy of mammograms nowadays is about 87%, i.e.,
mammograms correctly identify 87% of women who have breast
cancer. However, the false positive rate is about 10% for first
mammograms. Given that the prevalence of breast cancer in the adult
female population is about 12.4%, calculate the probability that a
woman actually has breast cancer given that she receives a positive
screening result at her first mammogram.
Essay question: For the mammogram scenario described previously,
suggest some methods to reduce the negative impact of false
positives. In particular, how would you educate an audience with a
wide range of quantitative reasoning skills in this regard?
Transcribed Image Text:The accuracy of mammograms nowadays is about 87%, i.e., mammograms correctly identify 87% of women who have breast cancer. However, the false positive rate is about 10% for first mammograms. Given that the prevalence of breast cancer in the adult female population is about 12.4%, calculate the probability that a woman actually has breast cancer given that she receives a positive screening result at her first mammogram. Essay question: For the mammogram scenario described previously, suggest some methods to reduce the negative impact of false positives. In particular, how would you educate an audience with a wide range of quantitative reasoning skills in this regard?
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