LACPrecious
I think you are missing the point. Just because you can open the JPG in Illustrator doesn't mean it magically becomes an editable vectorised graphic.
>> I don't have to redraw it, do I?<<
Probably yes - but you CAN use Photoshop to help, depending on what is in the image.
What the others are suggesting is to open the JPG in Photoshop, then use whatever tools you need to create selections of each differnt coloured area. Once you have made the first selection, go to the PAths palette and create a path from the selection. You can add new selections to this path. When all your selected areas have been saved a paths, export the paths to Ilustrator. This ceates an AI file which can then be opened in AI. However, once opened you will not see anything because there is no stroke on the paths. Select all and add a stroke. You can also remove the crop marks that come in automatically using this method. You may need to clean up the paths in Illustrator so that you can then colour the various regions they enclose. It's not an easy job if the original image consists of many components and is almost impossible if the original JPG was a photo.
But there really isn't any quick and easy way of converting a raster JPG into a vector file.