*Originally posted by: ***RaynorWolfcastle**
*Originally posted by: ***scorpmatt**

the probability of getting exactly 500 heads and 500 tails is going to be close to the probabilty of all heads or all tails. both very close to nil, I can't remember the exact equation to put that into. but I could have my calculator flip a coin 1000 times for you

No that's incorrect, there are much better chances of getting 500 tails and 500 heads than 1000 of one or the other. The reason is quite simple, there are many more "ways" to make a 50/50 split than there are to make a 0/1000 split.

Jaybert gave a good example of this. If the order mattered and you wanted a specific sequence of heads and tails then you would be correct.

To use something similar to Jaybert's example with 4 flips:

The only way to get 4 heads is: HHHH -> (1/2)^4 = 1/16

The only way to get 4 tails is: TTTT -> (1/2)^4 = 1/16

There are several ways to get 2 of each: HHTT, HTHT, HTTH, THHT, THTH, TTHH -> 6*(1/2)^4 = 3/8

There is only one way to get the sequence HTHT -> (1/3)^4 = 1/16

Hope that clears things up for you. BTW, this is a probability problem, not a statistics problem.