The correct word to fill in the blank is "few." The complete sentence would be: "She's lucky. She has few problems."

Explanation:
- "Few" is used with countable nouns (like "problems") to indicate a small number. It implies that the number of problems she has is small, which is why she is considered lucky.
- "Little" is used with uncountable nouns and would not be appropriate in this context because "problems" is a countable noun.

So, the sentence "She's lucky. She has few problems." means that she doesn't have many problems, which is a fortunate situation.