Probability for Three Randomly Chosen Numbers to be in AP

Given with an array of numbers ‘n’ and the task is to find the probability of three randomly chosen numbers to be in AP.

Example

Input-: arr[] = { 2,3,4,7,1,2,3 }
Output-: Probability of three random numbers being in A.P is: 0.107692
Input-:arr[] = { 1, 2, 3, 4, 5 }
Output-: Probability of three random numbers being in A.P is: 0.151515

Approach used in the below program is as follows −

• Input the array of positive integers
• Calculate the size of the array

• Apply the formula given below to find the probability of three random numbers to be in AP

  3 n / (4 (n * n) – 1)

• Print the result

ALGORITHM

Start
Step 1-> function to calculate the probability of three random numbers be in  AP
   double probab(int n)
      return (3.0 * n) / (4.0 * (n * n) - 1)
Step 2->In main()
   declare an array of elements as   int arr[] = { 2,3,4,7,1,2,3 }
   calculate size of an array as  int size = sizeof(arr)/sizeof(arr[0])
   call the function to calculate probability as probab(size)
Stop

Example

#include <bits/stdc++.h>
using namespace std;
//calculate probability of three random numbers be in AP
double probab(int n) {
    return (3.0 * n) / (4.0 * (n * n) - 1);
}
int main() {
    int arr[] = { 2,3,4,7,1,2,3 };
    int size = sizeof(arr)/sizeof(arr[0]);
    cout<<"probability of three random numbers being in A.P is : "<<probab(size);
    return 0;
}

Output

Probability of three random numbers being in A.P is: 0.107692