Incorrect Labels on 3 Jars

You have 3 jars. Each jar has a label on it: white, black, or white&black. You have 3 sets of marbles: white, black, and white&black. One set is stored in one jar. The labels on the jars are guaranteed to be incorrect (i.e. white will not contain white). Which jar would you choose from to give you the best chances of identifying the which set of marbles in is in which jar.

Question 2:
There are three rooms, and there are Princess, Flowers and Snake in those rooms. The doors of all the rooms have incorrect nameplates. i.e., the nameplate for the princess' room is not Princess. Similarly, the nameplate for the Flowers' room is not Flowers. You need to find the room of the Princess without going to the room of Snake. How do you find?

Approach:

Pick one marble from the B&W jar and that tells you everything. Assume you pull one white marble out of the B&W jar. You know from the problem that the B&W jar cannot hold the mixed set of marbles, so it can only hold the all white or all black set, thus your one white example tells you it holds the all white set.

Next, think about the jar labled black. From the problem, you know that it cannot hold the all black set, and you already know where the all white set is, so by process of elimination, it must hold the mixed set. Now you know for sure what two of the jars hold, so you know what the final jar holds.

Question 2:
Go to the room which has the nameplate Snake. That will not have Snake. If the room has princess, you are done. If the room has flowers, then go to the room which has nameplate flowers. Princess would be there in that room. [Since, Princess cannot be there in the room which has nameplate Princess