A newspaper on January 24,
1997, discussed the recommendation of a special panel concerning
mammograms for women in their 40s. About 2 % of women aged 40 to 49
years old develop breast cancer in their 40s. But the mammogram
used for women in that age group has a high rate of false positives
and false negatives; the false positive rate is 0.22 , and the
false negative rate is 0.24. If a woman in her 40s has a positive
mammogram, what is the probability that she actually has breast
cancer?
Homework Answers
Ans:
Given that
P(cancer)=0.02
P(no cancer)=1-0.02=0.98
P(+test/no cancer)=0.22
P(-test/cancer)=0.24
Now,
P(+test)=P(+test/cancer)*P(cancer)+P(+test/no cancer)*P(no cancer)
=(1-0.24)*0.02+0.22*0.98
=0.2308
P(cancer/+test)=P(+test/cancer)*P(cancer)/P(+test)
=P(+test/cancer)*P(cancer)/(P(+test/cancer)*P(cancer)+P(+test/no cancer)*P(no cancer))
Option D is correct.
P(cancer/+test)=(1-0.24)*0.02/0.2308=0.0659
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