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.
2.1 x 10 to the third power
By cosine rule, the length of the longer diagonal is sqrt(60^2 + 40^2 - 2 x 60 x 40 cos 132) = sqrt(8,411.83) = 91.7 cm
The other angle of the parallelogram is 180 - 132 = 48
The length of the shorter diagonal is sqrt(60^2 + 40^2 - 2 x 60 x 40 cos 48) = sqrt(1,988.17) = 44.6 cm
