Cheating on a test?

Here is a question someone recently asked me:  What’s the probability that two students taking a multiple choice test with 29 questions will get exactly the same wrong answers on 10 of the questions?

 

My answer?   Let’s restate this question to make it a lot simpler.  Can we assume they also got the same correct answers?   If so, then the question simply becomes, “What’s the probability that 2 students choose the same answer for all 29 questions?”
P(all same) = (1/4)^{29} = .000000000000000003

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