What are the odds?

[james_davis_nicoll]

I was helping assemble a wall unit yesterday. Each shelf is supported by four pegs that clip into the support frames. The manner in which the pegs attach to the supports has a chirality but by my count we used at least a dozen pegs before we discovered that they came in left and right-handed varieties (Also bent and unbent but we had extras).

How likely is it that we'd manage to pick out pegs with the correct chirality by luck for that long?