Puzzle from Fermat's Room

Three people guard two doors. You know that:

• one person always tells the truth;
• one person always lies;
• one person randomly decides whether to tell the truth or lie (assume lies and truth are equally likely);
• the three know amongst themselves who they are.

You can ask two questions to the people. The answer to which must either be yes or no. What question do you ask and who do you ask?

Some further rules for the more pedantic:

1. You cannot ask questions like "Will it rain tomorrow?", because neither the truth teller, nor the liar can be sure.
2. You cannot ask questions like "What would you answer if I ask you blablabla?", because if you ask the random liar they don't what their next answer will be.
3. You cannot ask something like "Will you answer No to this question?", because the truth-teller can't answer this question.
4. All decisions must be based on the yes and/or no answers only.
5. This puzzle is not about "how to find a way around the rules".