# Selecting random class from weighted class probability distribution

I have a solution that I've scratched out, but it's a tad messy:

First, let's say we have a random number from a uniform distribution we'll be using to select a random class from a class probability distribution:

r = 0.525325235325


And a list of classes, along with a corresponding list of values representing a class probability distribution for the four classes:

classes = ["w", "x", "y", "z"]

distribution = [0.1, 0.2, 0.3, 0.4]


Now, to get the cumulative probabilities:

b = [sum(distribution[0:x + 1]) for x in range(len(distribution))]
>>> b
[0.1, 0.30000000000000004, 0.6000000000000001, 1.0]


So far so good. Now, select a class by the weighted probability:

c = [y for y in b if y > r]
>>> c
0.6000000000000001


And to get the selected class:

selected = classes[b.index(c)]
>>> selected
'y'


Putting it all together:

r = 0.525325235325
classes = ["w", "x", "y", "z"]
distribution = [0.1, 0.2, 0.3, 0.4]

b = [sum(distribution[0:x + 1]) for x in range(len(distribution))]
selected = classes[b.index([y for y in b if y > r])]


This works well enough. The thing is, it will be called each time the class probability distribution is updated along with a complex code base – so efficiency matters.

Are there any ways I can make this code more efficient in terms of speed and/or memory usage (eliminating b without the expense of additional processing would be nice) in Python? Alternatively, is there an established algorithm for this problem that I've overlooked?