In small sample
s of independent event
s, it is unlikely to get perfect
. 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
- Roll it again (#3). The chance of rolling a number not yet rolled is
- Roll it again (#4). The chance of rolling a number not yet rolled is
- Roll it again (#5). The chance of rolling a number not yet rolled is
- 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
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
- Flip 4 coins
It is expected to get 2 of them to be heads, and two of them to be
tails. There are 24 (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
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