Two chemistry students who had partied all night instead of studying for their final exam tried to make up the test by lying about having a flat tire. The professor caught them in the lie with a question on the make-up test asking "Which tire was it?". To calculate the probability that the students would give the same incorrect tire, it is assumed the car has 4 tires and the students did not coordinate their answers, making the probability 1/16.

1. "At Duke University, two students had received A's in chemistry all semester, but on the night
before
the final exam, they partied all night, woke up too late, and missed the exam. Their excuse to the
professor was that they had a flat tire on the way to school, and they asked if they could take a
make-up test. The professor agreed, wrote out a test and sent the two to separate rooms to take it.
The first question (on one side of the paper) was worth 10 points, and they answered it easily.
Then they flipped the paper over and found the second question, worth 90 points: "Which tire
was it?"
What is the probability that both students would say the same thing? I think it is 1/16. Is that
right?"
(a) What do you think? Is it really 1/16 ?
Assumptions: The students did not have a flat tire. They lied and were caught by surprise, so
they
did not coordinate their answers in advance.
This is an old story, so we also assume that they did not have cell phones with texting.
We are referring here to a vehicle with four wheels.
(b) In addition to the assumptions listed above, what other fundamental assumption do we need
to
make in order to determine the required probability? Is it a realistic assumption?
Solution
a) I too think its 1/16

2. b) another fundamental assumption is that the car has 4 wheels which is a realistic assumption