simple maths task
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20 Nov 2007, 00:39
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Journals
U can throw the number 9 with 3 cubes (1...6) on 6 ways:
1,2,6; 1,3,5; 1,4,4; 2,2,5; 2,3,4; 3;3;3
the number 10 on 6 ways too:
1,3,6; 1,4,5; 2,2,6; 2,3,5; 2,4,4; 3,3,4
but the number 10 was thrown offener as the number 9, why?
1,2,6; 1,3,5; 1,4,4; 2,2,5; 2,3,4; 3;3;3
the number 10 on 6 ways too:
1,3,6; 1,4,5; 2,2,6; 2,3,5; 2,4,4; 3,3,4
but the number 10 was thrown offener as the number 9, why?
your answer follows from this fact I stated
It's because the probabilities are different.
For a throw like x, y, z, you get Perm(3)*Prob(A)*Prob(B)*Prob(C) = 3! * 1/6 * 1/6 * 1/6 = 1/36.
For a throw like x, y, y, You get 3 * 1/6 * 1/6 * 1/6 = 1/72
And finally, for x, x, x, you get 1/6 * 1/6 * 1/6 = 1/216
Thus, the least numbers repeat themselves, the more probable a throw is.
For 9 you have 3 xyz, 2 xyy and 1 xxx.
For 10 you have 3 xyz, 3 xyy.
Thus, since getting xyy is more probable than getting xxx, it is more probable to get 10 (but not by much).
For those who want the numbers:
Getting a 10: 12.5%
Getting a 9: 11.6%