2.32. [The weight of a positive] (Based on G. Ginzer, Calculated Risks, Sim nd S
ID: 3057910 • Letter: 2
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2.32. [The weight of a positive] (Based on G. Ginzer, Calculated Risks, Sim nd Schuster, 2002 and S. Strogatz NYT article, April 25, 2010.) Women aged 40 to 49 years of age have a low incidence of breast can- cer: the fraction is estimated at 0.8%. Given a woman with breast cancer has a mammogram. the probability of detection le. a positive man!mogram is estimated to be 90%. Given a woman does not have breast cancer, the probability of a false positive (i.e a false alarm) is estimated to be 7%. (a) Based on the above numbers, given a woman aged 40 to 49 has a mammogram, what is (b) Given a woman aged 40 to 49 has a positive mammogram, what is the conditional (c) For 1000 women aged 40 to 49 getting mammograms for the first time, how many are the probability the mammogram will be positive? probability the woman has breast cancer? expected to have breast cancer, for how many of those is the mamogram positive, and how many are expected to get a false positive?Explanation / Answer
2.32. [The weight of a positive] (Based on G. Ginzer, Calculated Risks, Sim nd Schuster, 2002 and S. Strogatz NYT article, April 25, 2010.) Women aged 40 to 49 years of age have a low incidence of breast can- cer: the fraction is estimated at 0.8%. Given a woman with breast cancer has a mammogram. the probability of detection le. a positive man!mogram is estimated to be 90%. Given a woman does not have breast cancer, the probability of a false positive (i.e a false alarm) is estimated to be 7%. (a) Based on the above numbers, given a woman aged 40 to 49 has a mammogram, what is (b) Given a woman aged 40 to 49 has a positive mammogram, what is the conditional (c) For 1000 women aged 40 to 49 getting mammograms for the first time, how many are the probability the mammogram will be positive? probability the woman has breast cancer? expected to have breast cancer, for how many of those is the mamogram positive, and how many are expected to get a false positive?
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