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Probability -- I Might Have Once Known How to Calculate This

Posted By: Bob Koca
Date: Monday, 25 August 2008, at 8:37 p.m.

In Response To: Probability -- I Might Have Once Known How to Calculate This (Marty Storer)

I didn't follow the explanation but it seems to work. Here is how might think about it without calculator:

Suppose we keep x = 20 and just change the roll from 55 to 52. Then (1/36)^8 * (35/36)^12 = (35^12)/ 36^20 becomes instead (2/36)^8 (34/36)^12 = (2^8*34^12)/36^20

Changing the 1 to 2 makes a much larger difference than changing the 35 to 34. It results in getting 5-2 8 times in 20 shakes about 200 times (cheated here) as likely as 5-5 8 times in 20 shakes.

Does taking away just one trial make it 1/200th as likely? You lose a factor of 34 and also a factor of 1.67 (cheated here) from changing the binomial coefficient. Not enough.

But taking away 2 trials overshoots worse. You would lose 34 * 34 * adjustment for different binomial coefficient.

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