뜻밖에 (ddeut-bak-gge) – unexpectedly
You can look at this word to have a very similar meaning to 갑자기, which means suddenly.
In a way, both words can be used to describe surprise.
However, you would usually only use 뜻밖에 if there is some sort of expectation beforehand.
On the other hand, 갑자기 can be used in any situation of surprise.
아침에 일기 예보는 날씨가 따뜻한다고 보고했지만 뜻밖에 너무 춥네.
This morning, the weather forecast reported that it will be warm but it is unexpectedly really cold.
그 학생은 날마다 열심히 공부하는데 이번 시험에 뜻밖에 잘 못 봤네.
That student studies very hard everyday but this test she did unexpectedly bad.