概率计算器

复制import itertools
from fractions import Fraction

# 古典概率：从 n 个球中不放回抽 k 个，求某特定组合的概率
n, k = 10, 3  # 10 个球中抽 3 个
total = len(list(itertools.combinations(range(n), k)))
favorable = 1  # 只有一种特定组合
print(f"古典概率: {Fraction(favorable, total)}")  # 1/120 ≈ 0.00833

# 条件概率：P(A|B) = P(A∩B) / P(B)
p_a_and_b = Fraction(1, 10)  # 假设已知
p_b = Fraction(1, 4)
p_a_given_b = p_a_and_b / p_b
print(f"条件概率 P(A|B): {p_a_given_b}")  # 2/5

# 贝叶斯定理：P(H|E) = P(E|H) * P(H) / P(E)
p_h = Fraction(1, 100)  # 先验概率 1%
p_e_given_h = Fraction(99, 100)  # 灵敏度 99%
p_e_given_not_h = Fraction(1, 100)  # 假阳性率 1%
p_e = p_e_given_h * p_h + p_e_given_not_h * (1 - p_h)
p_h_given_e = p_e_given_h * p_h / p_e
print(f"贝叶斯后验概率: {float(p_h_given_e):.4f}")  # 约 0.5

复制package main

import (
	"fmt"
	"math/big"
)

// 贝叶斯概率计算（使用有理数避免浮点误差）
func bayes(prior, likelihood, falsePositive *big.Rat) *big.Rat {
	// P(E) = P(E|H)*P(H) + P(E|¬H)*P(¬H)
	one := new(big.Rat).SetInt64(1)
	notPrior := new(big.Rat).Sub(one, prior)

	pE := new(big.Rat).Add(
		new(big.Rat).Mul(likelihood, prior),
		new(big.Rat).Mul(falsePositive, notPrior),
	)

	// P(H|E) = P(E|H)*P(H) / P(E)
	posterior := new(big.Rat).Quo(
		new(big.Rat).Mul(likelihood, prior),
		pE,
	)
	return posterior
}

func main() {
	// 疾病检测：先验 1%，灵敏度 99%，假阳性 1%
	prior := new(big.Rat).SetFrac64(1, 100)
	likelihood := new(big.Rat).SetFrac64(99, 100)
	falsePositive := new(big.Rat).SetFrac64(1, 100)

	posterior := bayes(prior, likelihood, falsePositive)
	fmt.Printf("后验概率: %s ≈ %.4f\n", posterior.RatString(), float64(posterior.Num().Int64())/float64(posterior.Denom().Int64()))
	// 输出: 后验概率: 1/2 ≈ 0.5000
}

复制// 古典概率：从 52 张牌中抽到特定牌的概率
function classicalProbability(total, favorable) {
  if (favorable > total) throw new Error('favorable 不能大于 total');
  return favorable / total;
}

console.log(classicalProbability(52, 4)); // 0.0769（抽到 A 的概率）

// 条件概率：P(A|B) = P(A∩B) / P(B)
function conditionalProbability(pIntersection, pB) {
  if (pB === 0) throw new Error('P(B) 不能为 0');
  return pIntersection / pB;
}

console.log(conditionalProbability(0.1, 0.25)); // 0.4

// 贝叶斯定理：P(H|E) = P(E|H) * P(H) / P(E)
function bayesTheorem(prior, likelihood, falsePositive) {
  const pE = likelihood * prior + falsePositive * (1 - prior);
  return (likelihood * prior) / pE;
}

// 疾病检测例子
const posterior = bayesTheorem(0.01, 0.99, 0.01);
console.log(posterior.toFixed(4)); // 0.5000