请教一下各类大佬, 这个概率题我错在哪里?
資深大佬 : gulu 3
""" 从目标集合 S 中有放回地抽取 n 次, 计算子集 s 中的每个元素至少抽中 1 次的概率. 目标集合 S 为 [A, A, B, C...] 这种有重复的集合. 集合 s 为 S 的子集, 且 s 中不包含重复元素. """ import time from typing import List from random import Random from functools import reduce def frac(n): """ n! """ if n <= 1: return 1 r = 1 while n > 1: r *= n n -= 1 return r def calculate_probability(choices: List[str], targets: List[str], num_draw: int) -> float: """ 计算此概率:从目标集合 choices 中有放回地抽取 num_draw 次, targets 集合中每个元素至少抽中一个. targets 必须是 choices 的子集 """ num_choice = len(choices) num_target = len(targets) left_draw = num_draw - num_target targets = {t: choices.count(t) for t in targets} if left_draw < 0: print(f"0.0%") return 0.0 # 目标集合每个选项出现的次数相乘, 为目标集合的可能数 count = reduce(lambda x, y: x * y, targets.values()) # 如果抽取次数大于目标集合个数, 则还可以再抽取若干次任意元素 count *= (num_choice ** left_draw) # 以上获得的可能数是固定顺序下的, 所以总的可能数需要再乘以 num_draw 的阶乘 count *= frac(num_draw) # 每次抽取有 num_choice 次可能, 总共抽取 num_draw 次 total = num_choice ** num_draw p = round(count / total * 100, 2) print(f"{p}%") return p def observe_probability(choices, targets, num_draw) -> float: """ 观察此概率:从目标集合 choices 中有放回地抽取 num_draw 次, targets 集合中每个元素至少抽中一个. targets 必须是 choice 的子集. """ rand = Random() rand.seed(time.time() * 1000) count = 0 total = 1000000 # 模拟 total 次 for num_test in range(total): targets = {t: 0 for t in targets} # 每次模拟抽取 num_draw 次 for draw in range(num_draw): choice = rand.choice(choices) if choice in targets: targets[choice] += 1 values = list(targets.values()) match = all(map(lambda x: x >= 1, values)) if match: # 所有目标都抽到, 计数加 1 count += 1 p = round(count / total * 100, 2) print(f"{p}%") return p def test(): choices = [ "A", "A", "A", "A", "B", "B", "B", "B", "C", "C", "C", "C", "D", "E", ] targets = ["A", "B", "C", "D"] num_draw = 5 observe_probability(choices, targets, num_draw) calculate_probability(choices, targets, num_draw) if __name__ == "__main__": test() 大佬有話說 (18)