Does a solution exist to the following riddle?

You meet three friends Alice, Bob, Christy.

Each has a different favourite colour, among red, green and blue. They know each other's favourite colour, but you do not.

One of them always tells the truth, one always lies, and one tells either a truth or a lie at random, decided by a fair coin flip, the outcome of which you do not see.
They all know who speaks in which way.

You are allowed a total of 3 yes-no questions, each question being asked to one person of your choice.

You may:
– ask one person multiple questions,
– ask two or more people the same question (each instance counts toward your total).

Question validity:
– Your questions must be clearly answerable with either 'Yes' or 'No,' without causing contradictions, paradoxes, or requiring non-binary responses.
– Questions must not rely on knowing or conditioning on the outcome of any coin flip. The flipper’s answer is considered truly random: neither you nor the other friends can infer anything from the flipper’s internal process, nor may a question attempt to "fix" the outcome of the coin flip by hypothetical reasoning (e.g., questions like “If next time the flipper speaks, they were to tell the truth, then...”)

Can you determine each friend's favourite colour, using no more than 3 yes-no questions as described?

Resolution Criteria:
– resolves Yes if a verified solution exists.
– resolves No if a verified proof shows no such solution is possible.
– resolves N/A if it is found to be not well-posed (e.g., if two reasonable interpretations lead to different conclusions).

As long as no agreement has been reached on a proof, this will remain unresolved (the close date may be postponed indefinitely).

Post the answer or a link to it if you think there is enough evidence to resolve it.