1979-built house, two bathrooms sharing a common wall, one plain
electrical outlet in each bathroom. Both outlets are on the same
circuit; i.e., one circuit breaker kills them both.

I want to install GFCI protection. Do I need to install one in each
bathroom?

Or is the downstream one protected by its upstream brother? If yes, how
do I determine which one is first in the circuit?

--
Wise men speak because they have something to say; fools because they
have to say something.
�ƒ Plato