Randomly assign a value to a specificed number of rows in a feature class in ArcGIS

I have several feature classes, each with a million or so rows. In each of these feature classes I have an attribute (“STATE”), the value of which I want to randomly assign to one or another state (so represented as a binary – 1 or 0).

However For each of these feature classes, there are only a specific number of rows (events) that can be assigned 1. Does anyone have a quick means of taking this field (currently, for all rows [STATE] = 0), and randomly assigning x number of rows to be [STATE] = 1. Say, turn 25,000 of the million rows to be 1 rather than 0?

I have tried using cursor but I keep failing at it.