The Serpent-Tail

Question

After defeating the octangular spirits, you find yourself needing some laundry powder. However, you can't find any at your usual shop, and so you have to ask one of the employees, who happens to be a serpent-tail. You know that serpent-tails have 5 tails, which can understand and answer questions, but only with cracks and slaps. The 5 tails each follow distinct rules, depending on the true answer:

Tail	Yes	No
A	Crack	Slap
B	Slap	Crack
C	Random	Random
D	Crack	Crack
E	Slap	Slap

What is the quickest (fewest questions on average) strategy to find out if the store has laundry powder in stock? You can ask a question to multiple tails at once

Answer 1

New answer: 1 question.

If I were to ask you if there was laundry powder in stock, would you answer with a crack?

Explanation:

If there is laundry powder, tail A answers "crack" to "is there laundry powder?" and "crack" to "would your answer be a crack?"; tail B answers "slap" and "crack". Thus either way, there are at least 3 answers of "crack" (counting tail D, not caring about the random). So if there are >= 3 cracks, the answer is yes. With similar logic >= 3 snaps means no.

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Outdated answer, for posterity

2 questions.

First question:

Are you a tail?

Now we will figure out who to ask the next question to:

The answer to Q1 is "yes". Two of the deterministic tails will slap and two will crack. The random tail will join one of those groups. Simply choose the two tails with the same response. They are guaranteed to not have a random tail in their group.

Now ask this group:

"Is laundry powder in stock?"

Explanation:

If you get two different answers, the true answer is "no" because the tail in your group which changes answer based on truthiness has just done so. (One tail in your group will give the same answer no matter what, but they don't matter right now). Using similar logic, if you get two of the same answer then the true answer is "yes"