--- id: 5e44414f903586ffb414c950 title: 概率计算器 challengeType: 23 forumTopicId: 462364 dashedName: probability-calculator --- # --description-- 假设有一顶帽子，里面有 5 个蓝球、4 个红球和 2 个绿球。 随机抽取的 4 个球中至少包含 1 个红球和 2 个绿球的概率是多少？ 虽然可以使用高等数学来计算概率，但更简单的方法是编写一个程序来执行大量实验来估计近似概率。 对于这个项目，你将编写一个程序来确定从帽子中随机抽取某些球的大致概率。 First, create a `Hat` class in `main.py`. 该类应该采用可变数量的参数来指定帽子中每种颜色的球数。 例如，可以通过以下任何一种方式创建类对象： ```py hat1 = Hat(yellow=3, blue=2, green=6) hat2 = Hat(red=5, orange=4) hat3 = Hat(red=5, orange=4, black=1, blue=0, pink=2, striped=9) ``` 一顶帽子总是至少有一个球。 创建时传递给 hat 对象的参数应转换为 `contents` 实例变量。 `contents` 应该是一个字符串列表，其中包含帽子中每个球的一个项目。 列表中的每一项都应该是一个颜色名称，代表该颜色的单个球。 例如，如果你的帽子是 `{"red": 2, "blue": 1}`，`contents` 应该是 `["red", "red", "blue"]`。 `Hat` 类应该有一个 `draw` 方法，该方法接受一个参数，该参数指示要从帽子中抽取的球数。 此方法应该从 `contents` 中随机删除球，并将这些球作为字符串列表返回。 在抽取过程中球不应回到帽子中，类似于没有放回的黑盒实验。 如果要抽的球数量超过可用数量，则返回所有球。 Next, create an `experiment` function in `main.py` (not inside the `Hat` class). 此函数应接受以下参数： - `hat`：一个包含球的帽子对象，应该在函数内复制。 - `expected_balls`：一个对象，指示尝试从帽子中抽取的确切球组以进行实验。 例如，要确定从帽子中抽取 2 个蓝球和 1 个红球的概率，将 `expected_balls` 设置为 `{"blue":2, "red":1}`。 - `num_balls_drawn`：每次实验中从帽子中抽出的球数。 - `num_experiments`：要执行的实验数量。 （进行的实验越多，近似概率就越准确。） `experiment` 函数应该返回一个概率。 例如，如果你想确定当你从一个包含 6 个黑球、4 个红球和 3 个绿球的帽子中抽出 5 个球时，至少得到 2 个红球和 1 个绿球的概率， 你将进行 `N` 次实验，记录其中你至少得到 2 个红球和 1 个绿球的次数 `M`，并估计概率为 `M/N`。 每个实验都包括从一个装有指定球的帽子开始，抽出几个球，并检查你是否抽到了你试图抽出的球。 以下是基于上面的示例调用 `experiment` 函数的方法，其中包含 2000 个实验： ```py hat = Hat(black=6, red=4, green=3) probability = experiment(hat=hat, expected_balls={"red":2,"green":1}, num_balls_drawn=5, num_experiments=2000) ``` The output would be something like this: ```bash >>> 0.356 ``` 由于这是基于随机抽取的，因此每次运行代码时概率会略有不同。 _Hint: Consider using the modules that are already imported at the top. Do not initialize random seed within the file._ # --hints-- Creation of `hat` object should add correct contents. ```js ({ test: () => { pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code); pyodide.FS.writeFile( "/home/pyodide/test_module.py", ` import unittest import probability_calculator from importlib import reload reload(probability_calculator) probability_calculator.random.seed(95) class UnitTests(unittest.TestCase): maxDiff = None def test_hat_class_contents(self): hat = probability_calculator.Hat(red=3,blue=2) actual = hat.contents expected = ["red","red","red","blue","blue"] self.assertEqual(actual, expected, 'Expected creation of hat object to add correct contents.') ` ); const testCode = ` from unittest import main import test_module from importlib import reload reload(test_module) t = main(module='test_module', exit=False) t.result.wasSuccessful() `; const out = __pyodide.runPython(testCode); assert(out); }, }); ``` The `draw` method in `hat` class should reduce number of items in contents. ```js ({ test: () => { pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code); pyodide.FS.writeFile( "/home/pyodide/test_module.py", ` import unittest import probability_calculator from importlib import reload reload(probability_calculator) probability_calculator.random.seed(95) def test_hat_draw(self): hat = probability_calculator.Hat(red=5,blue=2) actual = hat.draw(2) expected = ['blue', 'red'] self.assertEqual(actual, expected, 'Expected hat draw to return two random items from hat contents.') actual = len(hat.contents) expected = 5 self.assertEqual(actual, expected, 'Expected hat draw to reduce number of items in contents.') ` ); const testCode = ` from unittest import main import test_module from importlib import reload reload(test_module) t = main(module='test_module', exit=False) t.result.wasSuccessful() `; const out = __pyodide.runPython(testCode); assert(out); }, }); ``` The `experiment` method should return a different probability. ```js ({ test: () => { pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code); pyodide.FS.writeFile( "/home/pyodide/test_module.py", ` import unittest import probability_calculator from importlib import reload reload(probability_calculator) probability_calculator.random.seed(95) class UnitTests(unittest.TestCase): maxDiff = None def test_prob_experiment(self): hat = probability_calculator.Hat(blue=3,red=2,green=6) probability = probability_calculator.experiment(hat=hat, expected_balls={"blue":2,"green":1}, num_balls_drawn=4, num_experiments=1000) actual = probability expected = 0.272 self.assertAlmostEqual(actual, expected, delta = 0.01, msg = 'Expected experiment method to return a different probability.') hat = probability_calculator.Hat(yellow=5,red=1,green=3,blue=9,test=1) probability = probability_calculator.experiment(hat=hat, expected_balls={"yellow":2,"blue":3,"test":1}, num_balls_drawn=20, num_experiments=100) actual = probability expected = 1.0 self.assertAlmostEqual(actual, expected, delta = 0.01, msg = 'Expected experiment method to return a different probability.') ` ); const testCode = ` from unittest import main import test_module from importlib import reload reload(test_module) t = main(module='test_module', exit=False) t.result.wasSuccessful() `; const out = __pyodide.runPython(testCode); assert(out); }, }); ``` # --seed-- ## --seed-contents-- ```py import copy import random class Hat: pass def experiment(hat, expected_balls, num_balls_drawn, num_experiments): pass ``` # --solutions-- ```py import copy import random class Hat: def __init__(self, **hat): self.hat = hat contents = [] for i in hat: for j in range(hat[i]): contents.append(i) self.contents = contents def draw(self, number): drawn = [] if number >= len(self.contents): return self.contents else: for i in range(number): drawn.append( self.contents.pop(random.randrange(len(self.contents))) ) return drawn def experiment(hat, expected_balls, num_balls_drawn, num_experiments): expected_balls_list = [] drawn_list = [] success = 0 for i in expected_balls: for j in range(expected_balls[i]): expected_balls_list.append(i) for j in range(num_experiments): hat_copy = copy.deepcopy(hat) drawn_list.append(hat_copy.draw(num_balls_drawn)) exp_ball_list_copy = expected_balls_list[:] for k in range(len(drawn_list[j])): try: ind = exp_ball_list_copy.index(drawn_list[j][k]) exp_ball_list_copy.pop(ind) except: continue if len(exp_ball_list_copy) == 0: success += 1 probability = success/num_experiments return probability ```