[mfrommil]

n =/= 1

If a baseball player has 10 at bats, and gets 0 hits, he's 0/10, with n=10

If same baseball player has 500 at bats, and gets 0 hits, he's 0/500, with n=500

You can be a lot more confident that he won't get his 1st hit anytime soon from the 2nd case compared with the 1st case. Because the sample size is significantly larger, even though the # of successes is equal between the two cases.