Problem 1: The Little End of the Stick
If a stick is broken in two at random, what is the average
length of the smaller piece? What is the average ratio of
the smaller to the larger piece?
Source: Mosteller, Frederick, FIFTY CHALLENGING PROBLEMS IN
PROBABILITY WITH SOLUTIONS, 1965, Dover: New York.
Problem 2: The First Ace
Shuffle an ordinary deck of playing cards containing four aces.
Then, turn up cards from the top until the first ace appears.
On average, how many cards are required to produce the first ace?
Source: Mosteller, Frederick, FIFTY CHALLENGING PROBLEMS IN
PROBABILITY WITH SOLUTIONS, 1965, Dover: New York.
Problem 3: The Game of 26
Back in the days before it was banned by the mayor, you
could go into a Chicago bar and play the game of 26.
Therein, the player picks a number from 1 to 6, and
wins if that "point" comes up 26 or more times in 130
rolls of the dice (in practice, ten dice rolled
thirteen times).
What is the probability that you will win the Game of 26?
source: Scarne, John, SCARNE ON DICE
For solutions, and for more information about the
resampling/simulation approach to probability and
statistics (including software to do resampling
simulation), please send both your email and
"snail-mail" addresses to pcbruce at wam.umd.edu
(or call 703-522-2713), telling us which forums
you participate in.
