I actually laughed because what are the odds exactly that one piece I was looking for is missing?
Ordered a bag of +100 geometrical chain links for my autistic son to replace his ‘1 blue square’ that he lost 💀
I think the relevant math is a little different. The odds of a random single piece being a blue square are indeed 1/56, as you say. And you raised that to 99 to find the odds of still not having a blue square after 99 attempts, which is mathematically sound. But the wrong question.
Really, the odds of the blue square being missing from a new set of pieces are 1/56 times the probability that a set is missing a piece at all.
We have no way to know that for sure. But if we assume that 1/100 sets are missing a single piece, and the rest are missing no pieces (or have extras) then we expect 1/5600 sets to be missing the blue square.
Edit. That figure is 0.018%
Your comment assumes the set is supposed to contain 1 of each shape/color combination. Looking at the picture, it's plain to see that is not the case.
They just mix them all up at the factory, weigh out a certain amount, and bag that random assortment.
No my comment assumes there are 8 colors and 7 shapes that are randomly chosen.
But now that I look closer there are technically 9 colors and 8 shapes. I didn’t notice the ovals and the single purple.
The true odds may be closer to 1/7200
There are only 8 colors, and there are 3 purples.