I am unsure what the odds are of getting the background unfortunately. You will know though as soon as you open the gram if you've gotten the BG or not though
If you buy more than one gram i'd recommend viewing them in the old inventory with this link - (you need an account to see links)
This way you can see them all! Just click on the gram and you'll get a pop up window with a drop down box that shows you the items inside the gram for you to send. If you have the background it will be in that dropdown list.
Everyone don't forget you can send these to yourself! Just type in your own username and you will be the one who receives the gram ^^