The math behind all the discussion of the Powerball drawing assumes true randomness - equal likelihood for each number to be chosen, in the drawing.
Are those assumptions reasonable?
In the Powerball drawing, winning numbers are selected from two clear containers: one container has 69 white colored balls with each ball numbered in black ink with an integer from 1 to 69. The other container contains 26 red balls with each ball numbered in black ink with an integer from 1 to 26.
The balls are dropped into the respective containers and then mixed in the container by what appears to be air injected from the bottom of the container. The air is then turned off and a ball is raised from the bottom via a platform and then removed from the container. This procedure is repeated for the selection of each ball (five white and one red, the Powerball). Generally speaking, it seems reasonable that each ball is equally likely to be selected by this process.
It is possible - though its a stretch - that balls with printed numbers requiring more ink to delineate the number on the ball may weigh more due to the extra ink than balls requiring less ink. Coupled with gravity, this may be enough to keep those balls lower in the container and thus more likely to be picked by the platform. In short, the ball marked 68 may be more likely to be picked than the ball marked 1.
Luckily, this is a testable assumption. Studying the results from previous drawings would allow an assessment of whether each number is occurring with similar frequency. Without doing the statistical calculation and data collection, given the nature of this device for generating balls/numbers, its safe to assume that this process generates each number with equal probability.
