Has it ever been suggested that your random pulls are not random at all? In all reality you've probably noticed a pretty significant number of people that have been chosen multiple times as well as several that have not been chosen at all. This is an expected outcome if your random draws are truly random. Let's look at an example to explain how this happens.
Let's take a random pool consisting of 100 employees. On this first draw we want to test 20 people or 20% of the employees. 20% of 100 is the same as 1 in 5. When we do our second draw of 20%, how much overlap can be expected between the two draws?
Using the laws of probability, if you know the probability of two events happening separately, you can find the probability of them happening together by multiplying their individual probabilities. Using our example of 100 employees, randomly selecting 20, the probability of "Bob" getting selected is 1 in 5. The second draw is using the same number and percentages, 100 employees, selecting 20. The probability is once again 1 in 5 that "Bob" will be selected. To find out the probability of "Bob" being selected in both draws, you multiply the two probabilities, 1/5 x 1/5 = 1/25.
Therefore we can conclude that if we have an employee pool of 100 and we conduct 2 random draws of 20%, then we should expect to have 4 people selected in both draws. 100 x 1/25 = 4.