Newton-Pepys Problem
المؤلف:
Mosteller, F.
المصدر:
"Isaac Newton Helps Samuel Pepys." Problem 19 in Fifty Challenging Problems in Probability with Solutions. New York: Dover
الجزء والصفحة:
...
11-3-2021
2646
Newton-Pepys Problem
Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was more likely,
1. At least one six when six dice are rolled,
2. At least two sixes when 12 dice are rolled, or
3. At least three sixes when 18 dice are rolled.
The probability of obtaining 
or more sixes in a roll of 
dice is given by
where 
is a regularized hypergeometric function. Values for 
, 2, and 3 gives
(OEIS A143162 and A143163). Therefore, 
is the most likely, with 
asymptotically approaching 1/2 as 
.
REFERENCES:
Mosteller, F. "Isaac Newton Helps Samuel Pepys." Problem 19 in Fifty Challenging Problems in Probability with Solutions. New York: Dover, pp. 19 and 33-35, 1987.
Schell, E. D. "Samuel Pepys, Isaac Newton, and Probability." Amer. Statistician 14, 27-30, Oct. 1960.
Sloane, N. J. A. Sequences A143162 and A143163 in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في الاحتمالات و الاحصاء
اخر الاخبار
اخبار العتبة العباسية المقدسة
