\"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: %u201CWhich tire was it?%u201D 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 b) another fundamental assumption is that the car has 4 wheels which is a realistic assumption.

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: %u201CWhich
tire was it?%u201D
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
b) another fundamental assumption is that the car has 4 wheels which is a realistic assumption