Almost every family has their own car in China.

[diamondcutter]

1. Almost every family has their own car in China.
2. Almost every adult has their own smart phone in China.
(Made by me.)
Did I use the word “their” correctly in these two sentences?

 

[Barque]

Yes. They'd sound better with "in China" brought forward a little.
1. Almost every family in China has their own car.
2. Almost every adult in China has their own smartphone.

I'd have worded it differently however.
Almost every family in China has a car.
Almost every adult in China has a smartphone.

 

[diamondcutter]

What about using “its” instead of “their” like this?
Almost every family in China has its own car.

 

[Barque]

Yes, it's grammatical but I prefer "their" in this case.

 

[jutfrank]

I don't like your sentence 1, since the singular agreement has clashes with the plural their.

 

[diamondcutter]

2. Almost every adult has their own smart phone in China.

Does Sentence 2 have the same problem?

 

[Barque]

"Their" in this case isn't plural; it's a substitute for "his/her".

1. Almost every family has their own car in China.

You could get around the singular-plural clash if it bothers you by using "its" (for some reason, using "its" with "family" jars on me a little) or by rewording it to "Almost all families in China have their own car/a car of their own".

Again, it'd be simpler to just say "Almost all families in China have a car". (Is that really true by the way?)