Seven wayward students decided to spend the sunny afternoon at the beautiful Olana estate instead of going to statistics, unfortunately forgetting they had a major exam. They concoct a story, claiming...

Seven wayward students decided to spend the sunny afternoon at the beautiful Olana estate instead
of going to statistics, unfortunately forgetting they had a major exam. They concoct a story, claiming
that all commute together in a minivan and they had a flat tire. The professor agrees to give them a
makeup exam, on the provision that they all attend his office separately for the exam and cannot discuss
it with each other afterwards. When they each arrive in turn to take the exam, they find that it consists
of a single question, “Which tire was flat?” What is the probability that the duplicitous students would
pass the exam?