Re: Prime vs. prime cube action

In article <c7479e32-0158-4ccd-8563-6a0baa51fb07@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<pauldepstein@xxxxxxx> wrote:
If I remember rightly, you need to shake a pair of dice at least 24 or
25 times to have a >=50% probability of hitting a 66. However, many
people assume that because 18 = 0.5 * 36, a person is 50-50 to hit 66
in a series of 18 shakes. So hustlers have made money by offering an
even-money bet where the bet-taker bets on being able to hit at least
one 66 in 18 rolls.

Ah yes, I remember reading about this in a Martin Gardner article.

Another amusing problem along these lines is a roulette question that I heard
from Joe Buhler (presented here with some modifications of my own). Say I
bet a dollar on the number 1 at the roulette wheel. Win or lose, I then bet
a dollar on the number 2. Win or lose, I then bet a dollar on the number 3,
and so on around the wheel. I go around the wheel three full times, betting
a dollar each time. (I skip 0, of course; I'm also assuming there's no 00,
although I don't think it matters much for the question I'm asking.)

Question: What is the probability that at the end I'll be behind?

A. greater than 99%;
B. 90% to 99%;
C. 75% to 90%;
D. 50% to 75%;
E. less than 50%.

The problem is more fun if you try to guess the answer first before
calculating it in detail.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.

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