"Was your baby born?"
In plain form/casual talk certain particles are often omitted. か is often omitted when speaking and the intonation of the final syllable is raised. However, females tend to add in a の and raise the intonation of this instead. Take note that this is only ever in casual spoken conversation or when quoting such material.
The eternal question (again) is why is it は and not が? How do we know whether the baby is the topic or the subject (whatever that means)? It's が in the affirmative, so the baby's doing something (being born). It's は in this question, and who knows what it might be in the negative?
Answering my own question, four months later in my journey: は makes the question "Your baby, was it born?" (asking about whether the baby was born) が makes the question "Was it your baby that was born?" (asking about which baby it was. Or even, whether something other than a baby was born!)
This has to be the worst kind of english grammatical construction! In British english this question will mean "Was your baby born or did it die?" It means only that! I have no idea if that is a normal american way to ask if someone has had their baby YET! I can not question the japanese construction. I am learning that. Perhaps a native speaker can confirm if it doesnt literally translate to the Duo english or if it does, then would the japanese ask it that way in japanese!
As far as I can tell が is much more standard than は in this particular construction.
Tense is not formal or informal - the tense of a verb tells us when something happened or when something was done - in the past, the present, the future. You are thinking about the voice - the voice of a verb can be either active or passive. In this instance 生まれた is in the passive voice, however the verb is in a plain or informal/familiar form. My guess is that Duolingo wants us to speak politely by using at the very least the - ます form of verbs.
Thanks for pointing my mistakes. I need to learn English more. I agree with you that Duolingo might want us to speak politely, but I just recognized that it is not wrong, and that is why I wrote that comment. I am sorry for the lack of explainations. But now I think that their way to teach Japanese is appropriate, not to confuse us.
The problem is with the fact that in English the question, as idiomatically understood, implies that the baby already exists (as a baby, not a foetus), which in turn implies that the person asking using this tense wants to know whether the baby (a) was born or (b) came into existence by some other means, or (c) died in the womb!
The English translation is grossly wrong! To ask if a baby "was born" is to ask whether it was born or it came into existence by other means (e.g. was made in a lab, floated down from the sky, etc.) It's a ridiculous question that no person proficient in English would find themselves asking in any probable real-world situation. But that's not what the Japanese question intends. The intent of the Japanese question is to ask whether the baby HAS BEEN BORN YET, or is still in the womb. The correct translation should therefore be "Has your baby been born (yet)"