Help me stifle a neurotic mother (washer/dryer operation)?

I own a GE Model WWSE5200B washer and a GE DWSR405EB0CC dryer. My mother is under the impression one can not (and obsessively insists I do not) leave the house, even briefly mind you, when either one of the units are in operation. uming I am operating properly installed units, in a recently built, properly wired house and have modi of common sense (i.e.: follow the guidelines in the manual as to use), should I be concerned about leaving these appliances unattended. Am I right in concluding fire is a negligible threat hardly worthy of consideration? Does anyone have safety records with regard to these particular units or washers and dryers in general? Apparently my mother had some 'bad' experience with a smoldering dryer some 20 years ago, aren't modern appliances much safer. I'd like to be able to multi-task and not feel compelled to supervise these appliances when they are in use. Please help me shut her up before she drives me insane, a million thanks.