Same flat tire

Hello, I am unsure about how to solve this one:
It's Friday afternoon and six fraternity brothers at UNC have just attended their last class of the semester. To unwind before the final exam Monday morning, they decide to spend the weekend at the beach. After a weekend of immature, irresponsible behavior, they oversleep Monday morning and miss the final exam. Later that day they go to their professor (who received her Ph.D. from NC State) and explain that they went to the beach and were on the way back for the final exam but their car (a BMW of course) had a flat tire. The professor says that they can come back the next morning and she will give them a make-up final exam consisting of one short-answer question! The students are ecstatic and high-five each other all the way back to the frat house. The next morning the professor puts each student in a different room and hands them their one-question test. The question: Which tire?

What is the probability that all 6 students will say that the same tire was flat?

Hint: the answer is NOT (1/4)^6.


Ambassador to the humans
Nope! But now that I'm at ISU I'm obliged to say that clearly ISU is the better institution. Also you should join in on the chatbox at some point.
Can anyone help?
Four students failed to show up in Final Exam. They claimed that they shared a car on a field trip one week before the exam and had a flat tire, thus could not get back in time. They asked for a make-up exam. The professor agreed. He asks: Which tire? So, If all four of them claimed a same tire, how confident will the professor be to believe they are telling the truth?

My questions are:
1. Which one is the null hypothesis? Students told the truth or students lied?
2. What is the appropriate rejection region of the selected hypothesis test?
3. What is the Type I Error rate α of the rejection region you defined in the previous question?
4. Having collected the four students' answers, how do you define the p-value of such answers for this test?

Create your own thread for your own question.

Also, this looks like homework. Show how you have tried to solve the problems so far.