Answer:
However
Step-by-step explanation:
The two sentences are independent, but in a way they have some thought connection. They imply in contrary ideas: 'little chance of success' and 'enter the competition' and therefore the correct word to fill the blank is the adverb however (used when you are adding a piece of information that seems to disagree with what you just said). She had little chance of success. However , she decided to enter the competition.