In small
samples of
independent events, it is unlikely to get
perfectly
even distribution. This can be demonstrated in many ways:
 Roll an N sided dice N times.

 Roll a 6 sided dice once.
 Roll it again (#2). The chance of rolling a number not yet rolled is
5/6.
 Roll it again (#3). The chance of rolling a number not yet rolled is
4/6 (2/3).
 Roll it again (#4). The chance of rolling a number not yet rolled is
3/6 (1/2).
 Roll it again (#5). The chance of rolling a number not yet rolled is
2/6 (1/3)
 Roll it again (#6). The chance of rolling the remaining number that
has not been rolled is 1/6.
Thus, for rolls of a 6 sided dice, the chance of rolling 6 unique
numbers is the product (and) of each of the above
probabilities:
1 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6
This is 1.54% that on 6 rolls of the dice, that each number will appear
exactly once.
 Flip 4 coins

It is expected to get 2 of them to be heads, and two of them to be
tails. There are 2^{4} (16) ways to flip these four coins:
 T T T T : 1
 H T T T : 4
 H H T T : 6
 H H H T : 4
 H H H H : 1
While it is true that 2 heads and 2 tails is the most probable single
selection in that list, it is also the case that 2/3 of the combinations
are not the most likely.
It is true that over time, these events will
average out.
Approximately
1/6th of the dice rolls will be any given
number, and half of the coin
flips will be heads. This is not the case for small samples of these
events though.