There are three balls;one is white, another is blue, and the other is red.

He has three sons; one lives in Seoul, another lives in Ulsan, and the other lives in Busan.

There are a lot of bags; some are white, and the others are blue.

There are a lot of people; some are from America, others are from Japan, and the others are from the Philippines.
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Are the expressions above all grammatical? If there are any errors, would you correct them?

In each sentence, you should have a colon (:) instead of the semicolon (;).

In the first and second sentences, you should have semicolons where the commas are.

With the exception of punctuation, those sentences are correct. Please check the sites below so that you will better understand the difference in usage between colons and semicolons.

http://leo.stcloudstate.edu/punct/semicolon.html

http://leo.stcloudstate.edu/punct/colon.html

Idk but you should get that ball thing checked out. *slaps leg*

The expressions provided are not all grammatically correct. Here are the corrections:

1. There are three balls: one is white, another is blue, and the third is red. (Use "third" instead of "other.")
2. He has three sons: one lives in Seoul, another lives in Ulsan, and the third lives in Busan. (Use "third" instead of "other.")
3. There are a lot of bags: some are white, and the rest are blue. (Use "rest" instead of "others.")
4. There are a lot of people: some are from America, others are from Japan, and the rest are from the Philippines. (Use "rest" instead of "others.")