Domino drawing odds
July 20th, 2010 at 6:44:18 PM
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What are the odds that, given a full 28 tile double six set of dominoes, out of 5 randomly drawn dominoes, you will be able to make at least one 3 domino long line (where the connecting ends of each domino match)?
What about a 5 domino line out of 10 drawn? An X domino line out of Y drawn? (X and Y max out at 28, of course)
Example Draw:
I draw the 1-2, 2-6, 5-4, 2-2 and 0-6 dominoes from the set. I can make a line of three in the following ways:
1-2, 2-6, 6-0
1-2, 2-2, 2-6
0-6, 6-2, 2-2
Some back of the napkin calculations came up with a few cases (1 domino line out of Y <= 28 drawn = 100%, 2 domino line out of Y >= 8 drawn = 100%), but I admit my probability is a little rusty.
What about a 5 domino line out of 10 drawn? An X domino line out of Y drawn? (X and Y max out at 28, of course)
Example Draw:
I draw the 1-2, 2-6, 5-4, 2-2 and 0-6 dominoes from the set. I can make a line of three in the following ways:
1-2, 2-6, 6-0
1-2, 2-2, 2-6
0-6, 6-2, 2-2
Some back of the napkin calculations came up with a few cases (1 domino line out of Y <= 28 drawn = 100%, 2 domino line out of Y >= 8 drawn = 100%), but I admit my probability is a little rusty.
