Consider these as my pictures for the dice faces:
face1.png, face2.png, face3.png, face4.png, face5.png, face6.png
I would advise, using a JLabel (added to each panel) as it is 'simpler' to add a background to this without going into paint components. See below adding face1 to it.
JLabel lblDiceFaceOne = new JLabel();
ImageIcon diceFace = new ImageIcon("face1.png");
lblDiceFaceOne.setIcon(diceFace);
So you could have an array of the file paths and then randomly select an index from these.
String[] paths = {"face1.png", "face2.png".....};
Once you have the random number from 0 to 5 (what you rolled with 0 representing 1 and 5 representing 6) then you can set the label to this particular picture using the string file path. Clear the label first as shown below.
lblDiceFaceOne.setIcon(null); //clear the previous dice picture
lblDiceFaceOne.setIcon(new ImageIcon(paths[i])); //use random file path from array
This can be done for all 3 items inside your GUI whereby you can have a random number within the range and set this to the selected file path to use for the image. To clarify 'i' represents the random integer we got between 0 and 5.
Just an idea that could work for you and is relatively simple to implement.
If you do have to use JPanels then this might help for setting its background.