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21. Maggio 2008, 19:21:10
Kili 
What is the probability of getting a 10 double dices in a gammon-race of 45 moves and five of them double 6, in a real game?
Here is possible....

21. Maggio 2008, 20:21:17
alanback 
Argomento: Re:
Kili:  The probability is greater than zero.  Get over it.

21. Maggio 2008, 23:16:01
playBunny 
Argomento: Re:"Get over it"
alanback: Wow, that's rather uncharacteristically snappish! Chill out Karma Daddy-O!

21. Maggio 2008, 23:18:50
paully 
Argomento: Re:"Get over it"
playBunny: not like his more laid back easy going style on DG eh !!

22. Maggio 2008, 02:26:01
alanback 
Argomento: Re:"Get over it"
paully:   Actually, "Get over it" pretty much summarizes my approach to most problems :-)

21. Maggio 2008, 22:57:47
Thad 
Argomento: Re:
Kili: The probability of getting exactly ten doubles in 45 throws is (1/6)^10*(5/6)^35 = 2.79990879 × 10^-11.

The probability of getting exactly five double-6s in exactly ten doubles in 45 throws is (1/36)^6*(5/36)^4*(5/6)^35 = 2.89408577 × 10^-16.

Someone correct me if I'm wrong. ;-)

21. Maggio 2008, 23:02:35
alanback 
Argomento: Re:
Thad:  I think the relevant quantities in context would be ten or more doubles and five or more boxcars.  As far as your calcs go, I think the 10 doubles figure has to be multiplied by the combinations of 10 items chosen from 45, which I think is 45!/(10!*35!).  A comparable adjustment needs to be made to the second calc, but I don't have time to work it out :-)

22. Maggio 2008, 08:19:16
Thad 
Argomento: Re:
alanback: Right, I forgot the combination factors. Oops! Hurrying = Bad Math!! ;-)

22. Maggio 2008, 01:52:32
AbigailII 
Argomento: Re:
Thad: You are wrong.

The chance of rolling exactly 10 doubles in 45 rolls is (1/6)^10 * (5/6)^35 * C (10, 45), where C (x, y) gives you the number of ways to pick x elements from a set of y elements. Rolling exactly 5 double sixes, and exactly 5 other doubles out of 45 rolls happens with chance (1/36)^5 * (5/36)^5 * C (5, 45) * C (5, 40).

The former is slightly less than 9%, the latter is slightly more than 0.1%.

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