Four students decide they need an extra day to cram for a Monday exam. They leave town for the weekend, returning Tuesday. Producing dated receipts for hotel and other expenses, they explain that their car suffered a flat tire, and that they did not have a spare. The professor agrees to give them a make-up exam in the form of a single written question. The students take their seats in separate corners of the exam room, silently crowing over their deceptive triumph—until the professor writes the question on the blackboard: “Which tire?”

Assuming that the students had not agreed in advance on the identification of the tire in their story, what is the probability that all four students will identify the same tire?