1. A: What're your favorite sports?

B: Baseball.

2. A: What're your favorite sports?
B: Baseball and soccer.

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Are both questions and answers grammatical?

Even though we often pronounce "what are" like "what're," we don't write it that way.

What are your favorite sports?
Baseball, soccer, and golf. (Since the question is asking about SPORTS, which is plural, the answer should be plural in form, too.)

Both questions and answers are grammatical in both scenarios.

In the first scenario:
1. The question "What're your favorite sports?" is grammatical. It is a shortened form of "What are your favorite sports?" and follows correct grammar rules.
2. The answer "Baseball" is grammatical. It is a single sport and is written correctly.

In the second scenario:
1. The question "What're your favorite sports?" is grammatical, just like in the first scenario.
2. The answer "Baseball and soccer" is grammatical. It lists two sports, separated by "and," which is the correct way to combine them. Both sports are written correctly.