﻿I tested seven free online Binomial Probability Calculators on a difficult test case ------------------------------------------------------------------------------------ >> Note: "sealevel.info" is mine, but I tried to be fair and impartial << Test case (a real-world problem, as it happens): n=35750, k=20, p=1/9999 (or 0.0001000100010001 if entering a rational value for "p" isn't supported) Supports NAME "1/9999"? P(X = 20) ∑P(X ≤ 20) ∑P(X > 20) --------------------- -------- -------------------------- -------------------------- -------------------------- sealevel.info ("slow") Y 1.336562893500049e-9 0.9999999997288647 2.711353770861858e-10 (p=0.0001000100010001) * 1.336562893500046e-9 0.9999999997288647 2.711353770861854e-10 ("quick") Y 1.3365628935e-9 0.99999999973 2.7e-10 Casio Keisan (22 digits) Y 1.33656289350004855552E-9 0.9999999997288646229138 2.711353770861858284764E-10 (set k=21 to calc) (p=0.0001000100010001) * 1.336562893500046360045E-9 0.9999999997288646229138 2.71135377086185350827E-10 (set k=21 to calc) (30 digits) Y 1.3365628935000485555210338634E-9 0.999999999728864622913814171524 2.71135377086185828476351193568E-10 (set k=21 to calc) WolframAlpha Y 1.337e-9 1 - 2.711e-10 (set k=21 to calc) 2.711e-10 (which is 0.9999999997289) Harvey Berman N* 0 1 0 VassarStats Y <0.000001 >.999999 <0.000001 iCalcu N* 1.336562893519394e-9 0.9999999997424598 n/a (last 5 digits are wrong) (last 5 digits are wrong) Richard Lowrey Y "Sorry. Your value of n is too large." * means p=0.0001000100010001 instead of p=1/9999 All tests were run on March 1, 2024. Conclusions: 1. Casio Keisan is best. 2. My sealevel.info is second best. 3. WolframAlpha is third best. Dave Burton 3/1/2024 sealevel.info