Probability Game

Courtesy of a loyal reader:

Partying too hard and too late, the two top math students in a class overslept and missed the final exam. They told the professor they had a flat tire on the way, and asked if they might be allowed a make-up exam. The professor agreed. He then put them in separate rooms and gave each a written exam which consisted of 2 questions. The first question, noted as being worth 5% of the total exam score, was: What is the sum of 2 plus 2? The second question, noted as being worth 95% of the total exam score, was: Which tire was the flat tire? Question: What is the probability they both picked the same tire?

[EOP]