(June 4, 2011 at 8:23 am)FaithNoMore Wrote:(June 4, 2011 at 5:05 am)diffidus Wrote: Firstly, on a technical point, the probability of guessing 10 numbers in sequence is not 10^10. It is in fact 10!, which is equal to ~ 1 in 3.6 million. Following the rest of your argument this would mean at least one and likely two people on the planet would guess the correct sequence.How did you come to 10! as the answer? For some reason, my memory seems to tell me you're correct, but in trying to look up the answer it I could only verify my calculation. The probability of you guessing one digit is 1/10. The probability of you guessing 2 digits is 1/10 * 1/10 both numbers is 1 in 100 or 1/10^2. The probability of you guessing 3 digits in a row is 1/10*1/10*1/10 or 1/10^3. Therefore the probability guessing a sequence of of digits is 1/10^n, where n is the number digits you have to guess in a row. So in trying to guess 10 digits correctly the probability is 1/10^10.
Regardless if the probability is 1 in 3.6 million or 1 in 10 billion, would you let someone accused of a crime go based on either of those odds, or would you say with certainty he/she is guilty?
diffidus Wrote:On the second point, it is true that I have said holding an open mind reflects the facts as they are, but I have never said that this means you are unenlightened if you don't. In fact, it is in the nature of an open mind to respect all peoples beliefs where that facts are not fully known.I never meant to say that you were doing it intentionally, but you have started two threads of a similar manner. In both of those you have inadvertently come off condescending towards anyone who believes differently.
Diffidus:
It seems I owe you an apology on the mathematical question. I was assuming that you meant that each person would draw a different set of ten numbers i.e the second person would not draw the same numbers as the first and so on. However, with your extra explanation, I now see that you are allowing people to draw the same set of 10 numbers which would in fact be 10^10.