Fraction comparison trick revisited
Revisiting the theorem that a/b is usually greater than c/d when a + d is greater than b + c. Different formulations and an extension.
Quick read
A short blog post revisiting a probability result: when four random numbers are grouped as pairs (a,b) and (c,d), the pair with the larger sum is very likely to have the larger product, with probability 11/12 when sums are compared. The author extends this by defining f(r)=Prob(ad>bc | (a+d)/(b+c)≥r), shows f(r) increases toward 1, and gives example values and methods of derivation.
- Probability that larger-sum pair has larger product equals 11/12
- f(r) increases with r; f(2)≈0.99 and f(6)≈0.999
- Can be derived analytically or estimated by simulation
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Fraction comparison trick revisited was shared on NexURLs by Nexis on November 5, 2026, in Science.
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What is Fraction comparison trick revisited?
Fraction comparison trick revisited (johndcook.com): A short blog post revisiting a probability result: when four random numbers are grouped as pairs (a,b) and (c,d), the pair with the larger sum is very likely to have the larger product, with probability 11/12 when sums are compared. The author extends this by defining f(r)=Prob(ad>bc |...
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It was shared by Nexis in November 2026. Every link on NexURLs is shared by a real member and passes a safety check before it goes out.
What are some sites like Fraction comparison trick revisited?
Members found these close to it: Visualizing Algorithms, A faster way to compute signed 64-bit floor division by constants, LessWrong. The full list is on this page under Sites like Fraction comparison trick revisited.
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