三个随机选择的数字出现在 AP 中的概率
给定一个数字 n 和一个包含 1 到(2n+1)个连续数字的数组。随机选择三个元素。找出所选元素出现在 中的概率 :
Input : n = 2
Output : 0.4
The array would be {1, 2, 3, 4, 5}
Out of all elements, triplets which
are in AP: {1, 2, 3}, {2, 3, 4},
{3, 4, 5}, {1, 3, 5}
No of ways to choose elements from
the array: 10 (5C3)
So, probability = 4/10 = 0.4
Input : n = 5
Output : 0.1515
从(2n+1)个数字中选择任意 3 个数字的方法有:(2n+1)C3 现在，对于要在 AP 中的数字: 同差 1—{1，2，3}、{2，3，4}、{3，4，5}……{2n-1，2n，2n+1} 同差 2—{1，3，5 }、{ 2，4，6}、{3，5 (2n + 1)数中 3 个数的 AP 组总数为: (2n–1)+(2n–3)+(2n–5)+…+3+1 =n * n(前 n 个奇数之和为 n * n ) 所以，(2n+1)连续数中 3 个随机选择的数在 AP 中的概率= (n * n) / (2n + 1) C 3
C++
// CPP program to find probability that
// 3 randomly chosen numbers form AP.
#include <bits/stdc++.h>
using namespace std;
// function to calculate probability
double procal(int n)
{
return (3.0 * n) / (4.0 * (n * n) - 1);
}
// Driver code to run above function
int main()
{
int a[] = { 1, 2, 3, 4, 5 };
int n = sizeof(a)/sizeof(a[0]);
cout << procal(n);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find probability that
// 3 randomly chosen numbers form AP.
class GFG {
// function to calculate probability
static double procal(int n)
{
return (3.0 * n) / (4.0 * (n * n) - 1);
}
// Driver code to run above function
public static void main(String arg[])
{
int a[] = { 1, 2, 3, 4, 5 };
int n = a.length;
System.out.print(Math.round(procal(n) * 1000000.0) / 1000000.0);
}
}
// This code is contributed by Anant Agarwal.
Python 3
# Python3 program to find probability that
# 3 randomly chosen numbers form AP.
# Function to calculate probability
def procal(n):
return (3.0 * n) / (4.0 * (n * n) - 1)
# Driver code
a = [1, 2, 3, 4, 5]
n = len(a)
print(round(procal(n), 6))
# This code is contributed by Smitha Dinesh Semwal.
C
// C# program to find probability that
// 3 randomly chosen numbers form AP.
using System;
class GFG {
// function to calculate probability
static double procal(int n)
{
return (3.0 * n) / (4.0 * (n * n) - 1);
}
// Driver code
public static void Main()
{
int []a = { 1, 2, 3, 4, 5 };
int n = a.Length;
Console.Write(Math.Round(procal(n) *
1000000.0) / 1000000.0);
}
}
// This code is contributed by nitin mittal
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find probability that
// 3 randomly chosen numbers form AP.
// function to calculate probability
function procal($n)
{
return (3.0 * $n) /
(4.0 * ($n *
$n) - 1);
}
// Driver code
$a = array(1, 2, 3, 4, 5);
$n = sizeof($a);
echo procal($n);
// This code is contributed by aj_36
?>
java 描述语言
<script>
// Javascript program to find probability that
// 3 randomly chosen numbers form AP.
// function to calculate probability
function procal(n)
{
return (3.0 * n) /
(4.0 * (n *
n) - 1);
}
// Driver code
let a = [1, 2, 3, 4, 5];
let n = a.length;
document.write(procal(n));
// This code is contributed by _saurabh_jaiswal
</script>
输出:
0.151515
时间复杂度:O(1)
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