In the example the instructor uses, he mentions the probability for each person picking their correct name would be (1 / n) which in this case would be (1 / 8 billion). However, if names are being chosen from the bag, shouldn’t the population size decrease every time? For instance, for the first person to pull a name out it is (1 / 8 billion); for the second person it would be (1 / (8 billion - 1)), the next person (1 / (8 billion - 2)), etc.? Is there a difference between ‘expectation’ and probability?
Edit: Nevermind, I was mixing up the concept of probability and expected value
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