Hide Widget Everywhere but on a Member's Own Profile Page

Hello,

How could I make a widget appear only on a BuddyPress member's own member/profile page?

My theme has a "Member - Single Profile" widget area, but a widget placed there will appear not only on the logged in member's profile page, but also on any other member's profile page that she visits.

Example: Billie is logged in. On her member/profile page she sees the widgets that should appear. They are widgets that provide information about the logged-in user (Billie). This is good so far. But if Billie visits Liz's profile, Billie will still see the widget that should appear only on Billie's own profile page.

I've attached screen shots to hopefully make sure my description is clear.

Is there a solution for this?

Thank you!

James Wolfensberger