Some people find conditional probabilities confusing. They mix up the probability that an event A will happen given a condition that event B happened—P(A|B)—with the probability that an event B will happen given the condition that event A happened—P(B|A). This is known as the inverse fallacy, whereby people think that P(A|B) and P(B|A) must have similar probabilities. While you just saw that P(breast cancer by ninety | woman with BRCA mutation) is about 80 percent, by contrast P(woman with BRCA mutation | breast cancer by ninety) is only 5 to 10 percent, because many other people develop
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