recursive formula
 

I dont remember but there is a recursive formula for calculating the chance that six nines in a row occur this early in pi grecus (the Feynman Point so called)...can somebody explain to me how this probability is calculated?

If you treat each sequence of six digits like six numbers selected uniformly at random from 0-9, the chance that a given one is 999999 is 1/1000000, the chance it isn't is 999999/1000000, and the chance that none of the first 762 are is (999999/1000000)^762 = 0.9992.... But if there's nothing special about the 9, you might look at the chance that none of the first 762 starts a sequence of six digits all alike -- I trust you can find these odds?

odds
 

[QUOTE=CRGreathouse;517975]If you treat each sequence of six digits like six numbers selected uniformly at random from 0-9, the chance that a given one is 999999 is 1/1000000, the chance it isn't is 999999/1000000, and the chance that none of the first 762 are is (999999/1000000)^762 = 0.9992.... But if there's nothing special about the 9, you might look at the chance that none of the first 762 starts a sequence of six digits all alike -- I trust you can find these odds?[/QUOTE]




There is a recursive formula


the number can end in x (x different from 9)
can ends in x9, x99, x999, x9999,x99999


so the probability not to see six nines in a row in the first 762 digits let's call it 9T(762-1)


9T(761)=9T(760)+9T(759)+9T(758)+9T(757)+9T(756)


this should be the recursive formula but i am not sure


the problem is also to determine the values of T(761) ...

There is a very simple formula you can punch into a scientific calculator (you need an exponent key, not just a 4-function calculator, but nothing fancy). Look at my post.