JavaScript中二项分布实现错误排查请求：三个概率计算函数的数学与代码正确性校验

Hey everyone, I'm working on implementing three probability calculations in JavaScript and need a second pair of eyes to check both the math logic and code correctness. Right now, all three functions are returning inconsistent results, and I can't track down the bug in probability_three—it's giving 18.00% instead of the expected 9.75%.

Background & Formulas #

I'm implementing three probability formulas related to dice rolls:

1. Single outcome probability:
   P(d, n) = 1 - ((d - 1)/d)^n
2. Range of outcomes probability:
   P(d, n, o) = 1 - ((d - (d - o + 1))/d)^n
3. Binomial probability (exact k successes):
   P(d, n, o, k) = nCk * (p^k) * q^(n−k)
   Where:
   • nCk = combination of n things taken k at a time
   • p = probability of a single success
   • q = 1 - p

Combination (nCk) Implementation #

I based the combination function on standard factorial calculations:

function factorialize(num) { 
 // Step 1. Create a variable result to store num 
 var result = num; 
 // If num = 0 OR num = 1, the factorial will return 1 
 if (num === 0 || num === 1) return 1; 
 // Instantiate the while loop 
 while (num > 1) { 
 // Decrement by 1 
 num-- 
 // Update the result 
 result *= num 
 } 
 // Return 
 return result; 
} 
function nCr(n, r){ 
 // Compute n factorial 
 var nFact = factorialize(n) 
 // Compute r factorial 
 var rFact = factorialize(r) 
 // Compute n - r factorial 
 var nrFact = factorialize(n - r) 
 // Compute nCr 
 var result = (nFact / (rFact * nrFact)) 
 // Return 
 return result 
}

Function Implementations & Issues #

1. probability_one (returns 9.75% as expected) #

This calculates the probability of rolling at least one specific value across n dice with d sides:

function probability_one() { 
 // Get number of dice 
 var n = document.getElementById("n1").value 
 // Get sides on each die 
 var d = document.getElementById("d1").value 
 // Calculate 
 var prob = 1 - ((d - 1) / d)**n 
 prob = parseFloat(prob*100).toFixed(2)+"%" 
 prob = `<B>${prob}</B>` 
 // Print the probability 
 var p = document.createElement('p') 
 p.innerHTML = prob 
 document.getElementById("output1").appendChild(p) 
}

2. probability_two (returns 9.75% as expected) #

This calculates the probability of rolling at least one value in a range (defined by o) across n dice with d sides:

function probability_two() { 
 // Get number of dice 
 var n = document.getElementById("n2").value 
 // Get sides on each die 
 var d = document.getElementById("d2").value 
 // Get the specific outcome 
 var o = document.getElementById("o2").value 
 // Calculate 
 var prob = 1 - ((d - (d - o + 1)) / d)**n 
 prob = parseFloat(prob*100).toFixed(2)+"%" 
 prob = `<B>${prob}</B>` 
 // Print the probability 
 var p = document.createElement('p') 
 p.innerHTML = prob 
 document.getElementById("output2").appendChild(p) 
}

3. probability_three (returns 18.00% instead of expected 9.75%) #

This should calculate the binomial probability of getting exactly k successes (where a success is rolling a value that meets the o threshold) across n dice with d sides. I've added console logs to debug, but can't pinpoint the issue:

function probability_three(){ 
 // USER INPUTS 
 // Get number of dice 
 var n = document.getElementById("n3").value 
 // Get sides on each die 
 var d = document.getElementById("d3").value 
 // Get the value that defines a success 
 var o = document.getElementById("o3").value 
 // Get the number of success needed 
 var k = document.getElementById("k3").value 
 // CALCULATIONS 
 // p 
 var p = ((d - o) + 1)/10 
 console.log(`p: ${p}`) 
 // q 
 var q = (1 - p) 
 console.log(`q: ${q}`) 
 // nCr 
 var vnCr = nCr(n, k) 
 console.log(`nCr: ${vnCr}`) 
 // p**k 
 var pk = p**k 
 console.log(`p**k: ${pk}`) 
 // q**n-k 
 var pnk = q**(n-k) 
 console.log(`q**n-k: ${pnk}`) 
 // Probability 
 var prob = (vnCr * pk * pnk) / (p + q)**n 
 console.log(`Prob.: ${prob}`) 
 prob = parseFloat(prob*100).toFixed(2)+"%" 
 prob = `<B>${prob}</B>` 
 // Print the probability 
 var p = document.createElement('p') 
 p.innerHTML = prob 
 document.getElementById("output3").appendChild(p) 
}

I'd appreciate any help spotting where I went wrong with probability_three—either in translating the math to code or in the underlying logic. Let me know if you need more details about input values or expected behavior!

内容的提问来源于stack exchange，提问作者Mikitz06