"One way to visualize the drawing of a simple random sample is to think about the "hat model." Here is how it works. First, go to a good hat store and buy a big top hat. Next, make one slip of paper for each individual in the population, and place all of the slips in the hat, Make sure you use standard sized slips of paper so that they will all be the same shape, size, and weight. If there are 1,000 people in the population of interest, you will need 1,000 slips of paper. Now, let's say you want to obtain a simple random sample of 100 people. To make sure all the pieces of paper are thoroughly mixed in the hat, cover the top of the hat and shake it up vigorously. Next, select one slip of paper from the hat. After selecting the slip of paper, shake the hat up again to be sure the remaining slips are well mixed, and then select another slip of paper. After you have selected all 100 names, you will have a simple random sample size of 100 (n = 100) from a population size of 1,000 (N = 1,000). After you finish selecting the sample, you can look at the names to see who is included in the sample. These are the 100 people you will study."
For the purposes of creating a statistically-valid random sample - and assuming you follow instructions and mix it up well before pulling the first name - what is the benefit or justification for shaking the hat again after the first name is selected?