In the domino game Mexican
Train, holding a double can be a
problem, since when a double is
played, a second domino of the
same denomination must be played
immediately, or else a domino from
the bone pile must be drawn; and,
if it doesn’t match the double, you
lose control of your train.
The other
night, I was playing Mexican Train
with friends using a double 12 set
(a double 12 set includes every
two number combination from 0-0
through 12-12); and, in picking
a hand of 11 dominos, I got four
doubles.
What is the probability of
this?
A double-12 set has C(13,2) + 13 = 91 dominoes, of which 13 are doubles. You got 4 doubles out of a hand of 11.
The probability of getting exactly 4 doubles is:
13/91 * 12/90 * 11/89 * 10/88
* 78/87 * 77/86 * 76/85 * 75/84 * 74/83 * 73/82 * 72/81
* C(11,4)
= 5752263555729391/144115188075855872
=~ 0.0399143465205184
or about 1 in 25.
|
|
Posted by Charlie
on 2025-01-02 08:48:49 |
solution
