import numpy as np

def make_env(p_x):
  x = np.random.binomial(1, p_x, size=100*1000)
  y = np.logical_xor(x, np.random.binomial(1, 0.25, size=100*1000))
  return (x, y)

def p_x_given_y(env):
  xy = zip(*env)
  x_given_y = [x for x,y in xy if y]
  return np.mean(x_given_y)

env1 = make_env(0.5)
env2 = make_env(0.9)

print(p_x_given_y(env1)) # 0.7512315762181137
print(p_x_given_y(env2)) # 0.9634053658746433