jonj01 -> RE: What is the re-playability like for the scenarios ? (3/11/2014 1:18:25 AM)
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ORIGINAL: Barthheart quote:
ORIGINAL: jonj01 .... Now if the number list starts out at a different place the odds in rolling the same two six sided dies 5 times in a row...is 1/(36^5) or 1 to 60 million. .... This is the sequence (6,1,1,1,1) for times in a row. Or a probability of 1/(6^5^3) or about 1 to 2 trillion. ... These are not quite true because the odds of a die coming up a certain number have no effect on the next number the die will be. The odds of a normal 1d6 rolling a 1 is one in 6, the odds the next roll on the same die will be a 1 are 1 in 6 not 1/6^2. Given a perfectly balanced die and it is thrown exactly the same way every time, the chance that each roll will be a 1 is 1 in 6, because one roll has no effect on the previous roll. Sorry, this is incorrect for a sequence of die rolls. Use the penny toss as an example. Throw the penny 100 times the approximate probability BEFORE you throw a single penny toss that All 100 land heads is 1/(2^100). So the chances of throwing the sequence (6,1,1,1,1) on a six sided die...BEFORE...you roll a single die roll...is 1/(6^5). If you want the probability of doing it twice in a row BEFORE...you roll a single die roll it is 1/(6^5^2) and so on. You are right about the zero causal effect of the first roll on the second roll. But there have been people (I looked into this crap 2 years ago when I was playing VASL and don't remember the sources) who have run numeric simulators and it pretty much works out. The numeric simulator could roll 1's 6 times in a row the first try but when they count the number of tries and the number that 1 came up 6 times in a row..the numbers work out. They use this sequence analysis in determining the probability of winning the lottery (e.g. 1 /(40*39*38*37*36)) for a lottery having the numbers 1 through 40 and having to pick 5 numbers right, how many redundant systems they need in airplanes, forensic DNA analysis, etc. Its not exactly correct but it very close more times than it is very far. Given if you buy one lottery ticket and you win having only bought one lottery ticket..your chances AFTER the lottery draw are 1 in 1. But to give magnitude to probability of sequences occurring I've seen the above formula a lot.
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