RESAMPLING STATS

Ghermay Araya asmarina at next03epsl.wam.umd.edu
Tue Feb 15 09:28:46 EST 1994

```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