Does wet carpet in the bathroom become impure upon contact with a foot wet with madhy, and then the carpet is touched?

The prayer rug is not defiled by placing the foot on it unless you are certain that madhy (pre-seminal fluid) is present on the foot. The default state of things is purity. The foot is not defiled by touching inner garments unless you are certain that it came into contact with madhy while it (the madhy or the garment) was wet. One must not follow the whispers of doubts in these matters.