Question

Suppose that a simulation with a six-sided number cube provided these results during testing.

Outcome
1
2
3
4
5
6
Frequency
18
16
16
17
16
17
Is the number cube fair? Discuss the theoretical probability and how it compares to the simulation probability. The chart is above which is the outcomes and frequency.

Answer 1

Theoretical probability:
1 ... (16 and 2/3) %
2 ... (16 and 2/3) %
3 ... (16 and 2/3) %
4 ... (16 and 2/3) %
5 ... (16 and 2/3) %
6 ... (16 and 2/3) %

Experimental results:
1 ... 18
2 ... 16
3 ... 16
4 ... 17
5 ... 16
6 ... 17

The total number of rolls in the experiment was

(18 + 16 + 16 + 17 + 16 + 17) = 100

so the expected frequency for each outcome was 16-2/3 times,
and the SIMULATION probabilities were

1 ... 18%
2 ... 16%
3 ... 16%
4 ... 17%
5 ... 16%
6 ... 17%

To me, this looks fantastically close. The cube
could hardly be more fair than it actually is.