使用 JS 计算相关连续概率 n 次

Question

我有一个包含 n 种弹珠的数组，这是一个简化的例子：

 let marbles = [
   {variable: “Green marbles”, text: “Green marble”, amount: 10},
   {variable: “Yellow marbles”, text: “Yellow marble”, amount: 12},
   {variable: “Pink marbles”, text: “Pink marble”, amount: 8}
  ]

我希望使用这个数组来计算连续获得绿色、黄色或粉红色大理石而不替换它的概率（这意味着每次绘制大理石时它都是基板）。 举个例子：

in the first pick, the probability of getting a pink marble is: 
8/30.
In the second pick, the probability is now:
7/29 * 8/30
In the third pick, the probability is now: 
6/28 * 7/29 * 8/30

等等。 我已经设法做到这一点，以计算 with 替换的概率，如下所示：

let withReplacementArray = []
let i
let total = marbles.reduce((prev, cur)=> {return prev + cur.amount}, 0)
marbles.forEach((cur)=> {
for(i=1; i<=total; i ++) {
   withReplacementArray.push({
     probability: (Math.pow(cur.amount, i))/(Math.pow(total, i)),
     n: i, 
     text: cur.text
   })
 }
})

简而言之，这种方法不适用于计算没有放回的概率，因为它不再像将其提高到 i 次方那么简单。 有什么建议？ 或者有什么公式可以得到这个结果？

Answer 1

从循环内的两个弹珠数量（您感兴趣的类型和总数）中减去一个。为最后一个循环的累积概率保留一个外部变量，而不是幂。

let marbles = [
   {variable: "Green marbles", text: "Green marble", amount: 10},
   {variable: "Yellow marbles", text: "Yellow marble", amount: 12},
   {variable: "Pink marbles", text: "Pink marble", amount: 8}
];

// say we want to pick green
let greenAmount = marbles[0].amount;
let total = marbles.reduce((a, { amount }) => a + amount, 0);

let lastProbability = 1;
while (greenAmount > 0) {
  lastProbability = lastProbability * (greenAmount / total);
  console.log(lastProbability);
  greenAmount--;
  total--;
}
// 10/30
// then 10/30 * 9/29
// etc