# What probability methodology is electronic payment using?

Just curious. You pay electronically, and you get a string of numbers. My question, what is the likelihood for a person to type in the same serial number to say, top up their mobile credit? What is the range of probability electronic payment companies are using?Then, does electronic payment in China have longer serial number?

-
 Well, how many digits are there in the serial number? You also have a further combinatorial explosion if you include letters and other characters as well in the serial. – J. M. Dec 1 '10 at 4:14

Even assuming just the card number is required, assuming it is 16 digits (15 with AMEX), since each digit can be anything from $0-9$, there are $10$ possibilities for each place, and hence $10^{16}$ possible card numbers. The current population of the world is of the order of $10^{10}$. Even if everyone in the world owns a card issued by the same company, the chances of someone just "guessing" someone else's number are pretty slim (of the order of $10^{-6}$). Of course as I said above there are more security measures in place and most merchants generally don't allow multiple attempts to enter card info beyond a certain threshold.