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Aug 202011

Someone recently contacted me to ask the following question: What is the probability that two students, each taking the same multiple choice exam, with q possible answers per question, will get k or more identical answers in a row?

I initially imagined this to be straightforward. It’s just a sequence of n Bernoulli trials with p=1/q, with k successes, right? Probably just a few terms clumped with a binomial distribution? Oh, boy was I wrong. Go try it out.

MathWorld has an especially interesting solution:

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