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Eitaporra asked this question about How Not to Be Wrong: The Power of Mathematical Thinking:
A footnote from chapter 11 about the needles and slats states: "But this requires that the needle span the slat exactly; it is possible, but the probability that it happens is 0". I'm having a hard time understanding why the probability of the needle touching two cracks is zero. Could someone explain?
Greyson Intuitively the needle has an infinite number of positions in which it can lie touching zero or one cracks. The only case in which it spans the slat e…moreIntuitively the needle has an infinite number of positions in which it can lie touching zero or one cracks. The only case in which it spans the slat exactly is when it is perpendicular to the slat and the midpoint of the needle is directly between the cracks. This likelihood is vanishingly small compared to the entire set of possible orientations in which the needle will fall; hence, probability zero.(less)
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How Not to Be Wrong
by Jordan Ellenberg
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