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96 out of 1000 women without breast cancer will also get positive mammographies.If 1000 women in this age group undergo a routine screening, about what fraction of women with positive mammographies will actually have breast cancer?For example, the vast majority of doctors in these studies seem to have thought that if around 80% of women with breast cancer have positive mammographies, then the probability of a women with a positive mammography having breast cancer must be around 80%.Figuring out the final answer always requires pieces of information - the percentage of women with breast cancer, the percentage of women without breast cancer who receive false positives, and the percentage of women with breast cancer who receive (correct) positives.Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning. Maybe you're a girl looking for a boyfriend, but the boy you're interested in refuses to date anyone who "isn't Bayesian".They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and... What matters is that Bayes is cool, and if you don't know Bayes, you aren't cool.
800 out of 1000 women with breast cancer will get positive mammographies.What is the so-called Bayesian Revolution now sweeping through the sciences, which claims to subsume even the experimental method itself as a special case? Bayesian reasoning is very People do not employ Bayesian reasoning intuitively, find it very difficult to learn Bayesian reasoning when tutored, and rapidly forget Bayesian methods once the tutoring is over.What is the secret that the adherents of Bayes know? This holds equally true for novice students and highly trained professionals in a field.100 out of 10,000 women at age forty who participate in routine screening have breast cancer.80 of every 100 women with breast cancer will get a positive mammography.
The proportion of cancer patients with positive results, within the group of patients with positive results, is the proportion of (A) within (A C): 80 / (80 950) = 80 / 1030 = 7.8%.