>Now I just need to convince them of that.
Here, you have several options:
Try rolling a dice several times in a row, and write down how many time each number appears.
More realistic for your case: Try pulling out numbered cards from a closed container - mixed, and without looking. Make a total of 100 cards, and pull out 5 each time. Again, check how often each number appears.
Ask an expert in statistic to give his expert opinion on issues of "randomness".
Difference in opinions hath cost many millions of lives: for instance, whether flesh be bread, or bread be flesh; whether whistling be a vice or a virtue; whether it be better to kiss a post, or throw it into the fire... (from Gulliver's Travels)
