Question

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?

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

Answer 1

The probability that all 6 students will say that the same tire was flat is 1 out of 4096.

Step-by-step explanation:

The probability that all 6 students will say that the same tire was flat can be calculated using the concept of independent events.

Each student has 1 out of 4 tires that could be flat. So, the probability that a student picks the same tire as the previous student is 1/4.

The probability that all 6 students pick the same tire is:

P(all 6 students pick the same tire) = (1/4)*(1/4)*(1/4)*(1/4)*(1/4)*(1/4) = 1/4096

The probability that all 6 students will say that the same tire was flat is 1 out of 4096.