Put on your slick leather-soled dress shoes and walk down the carpeted stairs next time you're in your parents' house. You have to be extra careful that your foot doesn't slip down off the rounded edge of the carpeted step, don't you?

Those stairs would be much safer without the carpeting. They'd be easier to keep clean, too (ever try vacuuming the carpet on the stairs - now that's a nasty job).
 
Take a peek at what's under that carpeting. It might even be beautiful hardwood. If it isn't, it won't take much to paint the risers and put down safety treads.

While you're thinking of safety on the stairs, even though there may be a light at the top and the bottom, how dark would those stairs be if the power went off?  You may already have a few of these in places such as the kitchen and bathroom . . . At each stairway landing install a battery back-up night light that turns on immediately and automatically when the power goes off. No one will ever be left stumbling down the stairs in the dark or trying to hold on to both the railing and a flashlight. The cost is minimal and the improved safety will be enormous.