Why do some dialogue options have percentages next to them?

I noticed that some of my dialogue options have percentages next to them. Here's an example:

Not only does it have a percentage, but also an icon and it's highlighted green. What's special about it? What will happen if I choose this option?

Solution 1:

It is the chance that you will succeed at that dialog option (such as getting some extra money or items from the NPC).

Points in the Persuasion skill raise this chance.

I haven't run into any negative side effects with attempting and failing these sorts of checks, other than the fact that you don't get whatever bonus they would have given you, and you can't try again.

Solution 2:

Some dialog choices end with automatically selecting a secondary 'bad' choice. One example is when you meet up with a certain person. You can let them go free, fight them, or get a chance at making them pay you and let them go free. If you fail to make them pay you, you fight them instead of getting another chance to let them go free.