Samuel Pepys described dice labeled with the letters A, B, C, D, E, F instead of

Question

Samuel Pepys described dice labeled with the letters A, B, C, D, E, F instead of the numbers 1, 2, 3, 4, 5, 6. Then he posed the following question to Isaac Newton: “Peter a criminal convict being doomed to dye, Paul his friend prevails for his having the benefitt of one throw only for his life, upon dice soe prepared; with the choice of any one of these three chances for it, viz., One F at least upon six such dice. Two F's at least upon twelve such dice. or Three F's at least upon eighteen such dice. Question: - Which one of these chances should Peter in this case choose?" (Suggestion: Use a calculator, even though Newton didn't have one.)

Explanation / Answer

Peter should choose "One F at least upon six such dice" because the chances of getting at least one F in total 36 outcomes of six dice is higher than the chances of getting at least two F in total 72 outcomes of twelve dice or at least three F in total 108 outcomes of eighteen dice.

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