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260 lines
8.4 KiB
Markdown
260 lines
8.4 KiB
Markdown
---
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id: 5e44414f903586ffb414c950
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title: 概率计算器
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challengeType: 23
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forumTopicId: 462364
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dashedName: probability-calculator
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---
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# --description--
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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。
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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。
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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：
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```py
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hat1 = Hat(yellow=3, blue=2, green=6)
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hat2 = Hat(red=5, orange=4)
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hat3 = Hat(red=5, orange=4, black=1, blue=0, pink=2, striped=9)
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```
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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"]`。
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`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。
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Next, create an `experiment` function in `main.py` (not inside the `Hat` class). 此函数应接受以下参数：
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- `hat`：一个包含球的帽子对象，应该在函数内复制。
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- `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}`。
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- `num_balls_drawn`：每次实验中从帽子中抽出的球数。
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- `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。）
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`experiment` 函数应该返回一个概率。
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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。
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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：
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```py
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hat = Hat(black=6, red=4, green=3)
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probability = experiment(hat=hat,
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expected_balls={"red":2,"green":1},
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num_balls_drawn=5,
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num_experiments=2000)
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```
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The output would be something like this:
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```bash
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>>> 0.356
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```
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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。
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_Hint: Consider using the modules that are already imported at the top. Do not initialize random seed within the file._
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# --hints--
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Creation of `hat` object should add correct contents.
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```js
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({
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test: () => {
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pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
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pyodide.FS.writeFile(
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"/home/pyodide/test_module.py",
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`
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import unittest
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import probability_calculator
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from importlib import reload
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reload(probability_calculator)
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probability_calculator.random.seed(95)
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class UnitTests(unittest.TestCase):
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maxDiff = None
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def test_hat_class_contents(self):
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hat = probability_calculator.Hat(red=3,blue=2)
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actual = hat.contents
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expected = ["red","red","red","blue","blue"]
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self.assertEqual(actual, expected, 'Expected creation of hat object to add correct contents.')
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`
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);
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const testCode = `
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from unittest import main
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import test_module
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from importlib import reload
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reload(test_module)
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t = main(module='test_module', exit=False)
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t.result.wasSuccessful()
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`;
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const out = __pyodide.runPython(testCode);
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assert(out);
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},
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});
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```
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The `draw` method in `hat` class should reduce number of items in contents.
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```js
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({
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test: () => {
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pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
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pyodide.FS.writeFile(
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"/home/pyodide/test_module.py",
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`
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import unittest
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import probability_calculator
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from importlib import reload
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reload(probability_calculator)
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probability_calculator.random.seed(95)
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def test_hat_draw(self):
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hat = probability_calculator.Hat(red=5,blue=2)
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actual = hat.draw(2)
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expected = ['blue', 'red']
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self.assertEqual(actual, expected, 'Expected hat draw to return two random items from hat contents.')
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actual = len(hat.contents)
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expected = 5
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self.assertEqual(actual, expected, 'Expected hat draw to reduce number of items in contents.')
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`
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);
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const testCode = `
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from unittest import main
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import test_module
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from importlib import reload
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reload(test_module)
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t = main(module='test_module', exit=False)
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t.result.wasSuccessful()
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`;
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const out = __pyodide.runPython(testCode);
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assert(out);
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},
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});
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```
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The `experiment` method should return a different probability.
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```js
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({
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test: () => {
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pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
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pyodide.FS.writeFile(
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"/home/pyodide/test_module.py",
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`
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import unittest
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import probability_calculator
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from importlib import reload
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reload(probability_calculator)
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probability_calculator.random.seed(95)
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class UnitTests(unittest.TestCase):
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maxDiff = None
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def test_prob_experiment(self):
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hat = probability_calculator.Hat(blue=3,red=2,green=6)
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probability = probability_calculator.experiment(hat=hat, expected_balls={"blue":2,"green":1}, num_balls_drawn=4, num_experiments=1000)
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actual = probability
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expected = 0.272
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self.assertAlmostEqual(actual, expected, delta = 0.01, msg = 'Expected experiment method to return a different probability.')
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hat = probability_calculator.Hat(yellow=5,red=1,green=3,blue=9,test=1)
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probability = probability_calculator.experiment(hat=hat, expected_balls={"yellow":2,"blue":3,"test":1}, num_balls_drawn=20, num_experiments=100)
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actual = probability
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expected = 1.0
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self.assertAlmostEqual(actual, expected, delta = 0.01, msg = 'Expected experiment method to return a different probability.')
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`
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);
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const testCode = `
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from unittest import main
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import test_module
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from importlib import reload
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reload(test_module)
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t = main(module='test_module', exit=False)
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t.result.wasSuccessful()
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`;
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const out = __pyodide.runPython(testCode);
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assert(out);
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},
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});
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```
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# --seed--
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## --seed-contents--
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```py
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import copy
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import random
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class Hat:
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pass
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def experiment(hat, expected_balls, num_balls_drawn, num_experiments):
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pass
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```
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# --solutions--
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```py
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import copy
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import random
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class Hat:
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def __init__(self, **hat):
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self.hat = hat
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contents = []
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for i in hat:
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for j in range(hat[i]):
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contents.append(i)
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self.contents = contents
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def draw(self, number):
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drawn = []
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if number >= len(self.contents):
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return self.contents
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else:
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for i in range(number):
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drawn.append(
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self.contents.pop(random.randrange(len(self.contents)))
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)
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return drawn
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def experiment(hat, expected_balls, num_balls_drawn, num_experiments):
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expected_balls_list = []
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drawn_list = []
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success = 0
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for i in expected_balls:
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for j in range(expected_balls[i]):
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expected_balls_list.append(i)
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for j in range(num_experiments):
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hat_copy = copy.deepcopy(hat)
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drawn_list.append(hat_copy.draw(num_balls_drawn))
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exp_ball_list_copy = expected_balls_list[:]
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for k in range(len(drawn_list[j])):
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try:
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ind = exp_ball_list_copy.index(drawn_list[j][k])
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exp_ball_list_copy.pop(ind)
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except:
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continue
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if len(exp_ball_list_copy) == 0:
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success += 1
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probability = success/num_experiments
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return probability
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```
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