General Note:

In any situation in which two or more individuals are chosen from a large population of unspecified size, we will assume that the selections are independent events.

As a practical matter, this is a reasonable assumption, even though it is not strictly correct. For example, suppose that among a certain group of 1,000,000 people, there are exactly 165,000 who are left-handed. Suppose further that we randomly select two people from the group. The probability that the first selectee is left-handed is 165,000/1,000,000. However, the probability that the second person is left-handed depends on whether or not the first person was left-handed. If the first person was left-handed,, the probability of the second person being left-handed will be 164,999/999,999; on the other hand,, if the first person wasn't left-handed, the probability that the second person will be left-handed is 165,000/999,999. Since the probability of the second event is affected by the occurrence of the first event, these events are actually dependent.

Notice however, that 165,000/1,000,000 = .165000000

164,999/999,999 = .1649991649

165,000/999,999 = .165000165

The fact that these three numbers are all nearly equal to one another explains why, as a practical matter, it is reasonable to treat the two events as independent. The amount of error introduced by this technically incorrect assumption will not be significant.