Probability A Very Short Introduction

mind-and-cognition

• Turn the problem round: given the total score is eight, what is the chance the first throw yielded three? The answer is far less obvious, but Bayes' Rule finds it.

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• Bayes' Rule reduced the chance of Down's to 1 in 120, but amniocentesis carries a 1 in 200 risk of miscarriage. Should the parents take the test?

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• Whichever marble is chosen, we do not express surprise, even though an outcome with probability one in a trillion has occurred. But it did happen.

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faith-and-doubt

• The T/E ratio varies naturally across a menstrual cycle or with flu. Set the critical threshold too high and no cheating athlete is ever caught.

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• Six double-yolked eggs seems astonishing — unless the supermarket deliberately fills boxes from a batch, making the eggs far from independent.

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transformation

• We take the subjective approach as default, but hold opinions more firmly when backed by objective or frequency arguments — belief disciplined by evidence.

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