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?
The previous solutions are very good. I'll just add a little context.
https://en.wikipedia.org/wiki/Hypergeometric_distribution
For this problem N=91, K=13, n=11, k=4
C(13,4)*C(78,7)/C(91,11) = 0.3999
The first textbook I used to teach high school statistics back in the '90s included this distribution. Stats at this level usually boils down to approximation to a normal distribution. As long as n<<N, this is well approximated by a binomial, and from there by the normal. I don't think AP Statistics includes it, though.
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Posted by Jer
on 2025-01-02 11:33:32 |
Further comment
