Isaac Newton once settled a dice bet a friend couldn't work out for himself
In 1693, diarist Samuel Pepys wrote to Isaac Newton asking which is more likely: rolling at least one six with 6 dice, at least two sixes with 12 dice, or at least three sixes with 18 dice. Most people guess the three are equally likely, since the ratio of dice to required sixes stays constant. Which did Newton say was actually most likely?
Reveal the answer
The first option, at least one six in six dice, is slightly most likely, at about 66.5%, versus roughly 61.9% for the 12-dice case and 59.7% for the 18-dice case. Newton worked this out with exact probability calculations, correcting Pepys's intuition that more dice should make the stronger requirement easier to hit.
— Isaac Newton, Samuel Pepys, Newton-Pepys problem — Correspondence, 1693