The dwarves do not trust Bilbo to be a good burglar; they welcome him based on Gandalf's confidence.
The conflict is their mistrust of Bilbo, however, based on Gandalf's trust, they decide to take him with them, and he turns out to be a great burglar once he finds the Ring.
The other options are incorrect - Gandalf is not a problem drinker; the goblins don't live in the Misty Mountains; Bilbo didn't decide to stay home but rather he went with the dwarves.
The dwarves do not trust Bilbo to be a good burglar, they welcome him based on Gandalf's confidence. I hope this helps
