(Solution) - Each time a class meets the professor selects one student -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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Each time a class meets, the professor selects one student at random to explain the solution to a homework problem. There are 40 students in the class, and no one ever misses class. Luke is one of these students. What is the probability that Luke is selected both of the next two times that the class meets?