SOLUTION: Hi! I have a probability question: Two buddies are meant to take an exam in the morning. Instead of studying and resting the night before, they go out to a local pub and have

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Question 435552: Hi!

I have a probability question: Two buddies are meant to take an exam in the morning. Instead of studying and resting the night before, they go out to a local pub and have one drink too many. They oversleep their exam. They then go to the professor the next day with the following excuse.They explain that a friend out of town had an emergency and they needed to drive out to help.
On the way back, they claim a tire popped and they could not get back in time to take the exam. The professor allows the two to take the exam and writes a new exam for the students.He puts the two in different rooms. The exam has only one question with no partial credit.The question reads: "Which tire?" What is the probability that the students pass the exam?
Thank you for your help!
Found 2 solutions by shree840, robertb:
Answer by shree840(260) (Show Source):
You can put this solution on YOUR website!
1/4*1/4=1/16 ans provided there are only 4 tires on the car ANS

Answer by robertb(4012) (Show Source):
You can put this solution on YOUR website!
I will assume that both of them will pass the exam ONLY IF their answers are the same (in which case it will convince the professor that they really had a flat!). Student 1 has 4 choices, and student 2 has also 4 choices. Hence there are 4*4 = 16 ways for the 2 students to give their answers. Of these, there are only 4 ways that both of them could give the same answer. Thus the probability that the students pass is 4/16, or 1/4.