import sys
import random
import numpy

def between(tested,lo,hi):
  return (tested>=lo) and (tested <= hi)

def makeProjects():
   return numpy.random.normal(755,319,9)

def allocate(projects,categories):
  ratios = [0]*len(categories)
  allocation = [result.tolist().index(1) for result in numpy.random.multinomial(1,categories,size=9)]
  for cat in range(len(categories)):
    inCat = [projects[index] for index in filter(lambda index: allocation[index] == cat, range(len(projects)))]
    ratios[cat] = sum(inCat)/sum(projects)
  return ratios

def matchesCategories(projects,error):
  categories = [.02, .03, .20, .29, .46]
  ratios = allocate(projects,categories)
  ratios.sort()
  matches = [between(comp[0],comp[1]-error,comp[1]+error) for comp in zip(ratios,categories)]
  return all(matches)

def simulateProjects(nb,error):
  print 100.0*len(filter(lambda x: matchesCategories(makeProjects(),error),range(nb)))/nb

nb=1000
err=0.01

if len(sys.argv) > 1:
  nb = int(sys.argv[1])
if len(sys.argv) > 2:
  err = float(sys.argv[2])

simulateProjects(nb,err)