In A mode you're specifically selecting the f/stop. The camera will then measure the available light and accounting for the set ISO, calcualte and set the shutter speed required for correct exposure. Throughout this process the f/stop stays locked where you have set it -- A mode priority.
In P mode the same measuring process takes place. The camera meter calulates the correct exposure by measuring the available light and, accounting for the set ISO, it determines a shutter speed and f/stop combination. This determination is in not at all random, but based on a program embedded in the camera's software. This program is biased toward shutter speeds sufficiently fast enough to allow hand-held photogrpahy.
With your camera, as is typical of modern electronically controlled cameras, you can simply rotate a wheel on the camera and force the camera to rotate through the entire set of shutter speed, f/stop combinations available with your camera body and lens that will produce the same exposure. This is in fact the most efficient method of using the camera provided you intend to rely on the camera's internal metering system.
Put the camera in P mode and then select the f/stop/shutter speed combination that you assess as most appropriate for the photo.
Back to your original question: If in A mode on a sunny day with the ISO set to 100 you set the f/stop to f/11 the camera should select a shutter speed close to 1/250 sec. which would be a correct exposure. In P mode on a sunny day with the ISO set to 100 the camera will select both an f/stop and shutter speed for correct exposure. If you rotate the control wheel until the f/stop is f/11 you'll find the shutter speed is exactly the same as if you had set the camera to A and locked the f/stop at f/11. So it's really a case of how you want to approach or think about controlling the camera. The end result is the same.
Joe