"A dirty mug"
Translation:Một cái ca dơ
How do we know when it wants "một" included and when it doesn't when it says "a" something rather than "one" of something?
In some parts of the country, people say "cái cốc" instead of "cái ca". So that means "cốc" and "ca" are interchangeable in most cases. I believe the VN team has made a mistake in "Một cốc dơ" when it should be "Một CÁI cốc dơ". You can say "Một cốc dơ" in a very different context though.
What I meant in the second part of my answer is that "Một cốc dơ" can only be understood as "One/A mug is dirty", not "One/A dirty mug".
"Một CÁI cốc dơ", on the other hand, can be understood as either "One/A mug is dirty" or "One/A dirty mug".
There you see the importance of classifiers (cái, con, chiếc, ...) in Vietnamese.
Bạn so sánh nghĩa giữa "Một cốc dơ" và "Một CÁI cốc dơ" thì sẽ hiểu ý mình.