Here with a better explanation:

For Example: X, Y, Z are the women

Condition is all of them have raised their hands, means all of them have seen
atleast one person's forehead marked with "RED"

Now, lets say "X" is the person who has answered her forehead's colour.

How:

if X == WHITE

then Y & Z must be RED, to satisfy the above condition as :

X can see either Y or Z forehead colour as "RED"
Y can see only Z as X has WHITE
Z can see only Y as X has WHITE

In this scenario, very next moment, either of them i.e. Y or Z could have answered their own
forehead's colour as "RED".

But they didn't answer instead the answered person is "X", it means

Either Y or Z has raised their hand by seeing X's forehead's colour as "RED" and
not seeing each other's forehead's colour as "RED".

So, this makes X to answer that her forehead is marked with "RED" !!