Using bar soaps and hand towels won't have a greater chance of making you bleed, but razor blades and toothbrushes do since people usually cut themselves when shaving and toothbrushes can make your gums bleed.
I hope this helps.
Answer:
The most recent common ancestor of all currently living organisms is the last universal ancestor, which lived about 3.9 billion years ago. ... 6,331 groups of genes common to all living animals have been identified; these may have arisen from a single common ancestor that lived 650 million years ago in the Precambrian.
