Depending on how the serial number was chosen, the odds could be dramatically higher, dramatically lower, or zero. If the serial number was derived from another, new bill, received from a local bank, then the odds are quite good.

If it is chosen by writing the serial number of a bill in your pocket, then circulating the bill by purchasing something. The odds go up if you happen to stop by the banks a few days after that happened, or they go to zero if the bill was not fit for circulation and it was removed by the Federal Reserve.

Also, there's a good chance that a random serial number is not actually valid.