I needed to write a weighted version of random.choice (each element in the list has a different probability for being selected). This is what I came up with:
If your list of weighted choices is relatively static, and you want frequent sampling, you can do one O(N) preprocessing step, and then do the selection in O(1), using the functions in this related answer.
# run only when `choices` changes.
preprocessed_data = prep(weight for _,weight in choices)
# O(1) selection
value = choices[sample(preprocessed_data)][0]