Newton–Pepys problem
Probability problem / From Wikipedia, the free encyclopedia
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The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice.[1]
In 1693 Samuel Pepys and Isaac Newton corresponded over a problem posed to Pepys by a school teacher named John Smith.[2] The problem was:
Which of the following three propositions has the greatest chance of success?
- A. Six fair dice are tossed independently and at least one "6" appears.
- B. Twelve fair dice are tossed independently and at least two "6"s appear.
- C. Eighteen fair dice are tossed independently and at least three "6"s appear.[3]
Pepys initially thought that outcome C had the highest probability, but Newton correctly concluded that outcome A actually has the highest probability.