Joseph Meehan wrote:
If you have a hair dryer old enough to not have a polarized plug, I
would buy a new safer one. The old one is more likely to soon experience
other problems as well.

For a hairdryer, I think this is good advice. New hairdryers come with
GFCI built-in (and you should have GFCI in your bathroom plugs now anyway).

Even if you say your wife knows how to handle herself around the sink
(surely not the bathtub!), you may have children or relatives around at
some point.