Let $f:X\dashrightarrow Y$ be a rational map, where $X,Y$ are reduced and irreducible varieties over a field of characteristic zero.

Is the general fiber of $f$ always reduced?

Let $f:X\dashrightarrow Y$ be a rational map, where $X,Y$ are reduced and irreducible varieties over a field of characteristic zero.

Is the general fiber of $f$ always reduced? Is this true if we assume that the general fiber of $f$ has dimension zero?