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15:03, 30 April 2017
While it is true that drawing a single E is more likely than drawing a single A, the math for calculating the probability of a word is more complicated than that. You can't just start calculating with the assumption that BEILRS has been drawn; those letters themselves factor into the calculation, and they are not independent events. In this case, we can reduce the difference between BAILERS and BELIERS to the difference between drawing AE or EE when drawing two tiles from the bag.
If you draw two tiles out of a full bag, the probability of drawing two Es is much lower than the probability of drawing an A and an E. That is because there are 9 x 12 = 108 ways to draw an A and an E if you draw two tiles. But there are only (12 x 11) / 2 = 66 ways to draw two Es if you draw two tiles. This number of combinations is called "12 choose 2", and is explained in more detail in this [https://en.wikipedia.org/wiki/Combination Wikipedia article ] about combinations.
To reduce this to a simple example where it's easy to enumerate all the possibilities, consider a 4-tile bag containing only AAEE. I'll label the tiles A1, A2, E1, E2 for convenience. There are 6 possible ways to draw two unordered tiles: