I didn't want to use a public account (Omniref only accepts Github, Google, and FB) asking this question, so can someone here help me with the probability expla

I didn't want to use a public account (Omniref only accepts Github, Google, and FB) asking this question, so can someone here help me with the probability explanation? Consider the simplest non-trivial example: a sample of 1 element, from a two-element reservoir. At iteration one, we accept the first element. At iteration two, if the sample is to be random, we have to decide to keep the new element with a probability of 1/2: First element: (1/1) (1/2) = 1/2* Why are we multiplying the acceptance of the first element with the probability of keeping it? And then... But what if we're sampling from a pool of three elements instead? We know that we therefore have to keep the new element with a probability of 1/3…which means that we need to keep the element we already have with probability 2/3: First element: (1/2) (2/3) = 1/3* Where did the 1/2 come from? Why is it not 1/1 here?