title: Probability Three Randomly Chosen Numbers Ap
signature: double probabilityThreeRandomlyChosenNumbersAp(int n) {
test_code: #include <algorithm>
  #include <assert.h>
  #include <cstdlib>
  #include <iostream>
  #include <map>
  #include <set>
  #include <string>
  #include <tuple> 
  #include <unordered_map>
  #include <vector>
  #include <math.h>
  #include <cmath>
  #include <bits/stdc++.h>
  #include <numeric>
  #include <functional>
  
  using namespace std;
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(double actual, double expected){
      return abs(actual - expected) < 1e-09;
  }
  
  string driver(int n, double expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(n), expected)){
              return "PASSED";
          }
          return "FAILED";
      }
      catch (const std::overflow_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::runtime_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::exception& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (...)
      {
          return "UNK_ERROR";
      }
  }
  
  int main() {
      string result = "";
  
      result = driver(46, 0.0163062743707905); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver(5, 0.15151515151515152); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver(44, 0.017047655947307245); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver(15, 0.05005561735261402); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver(72, 0.010417169037858692); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver(2, 0.4); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver(86, 0.008721225027887637); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver(17, 0.04415584415584416); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver(30, 0.025006946373992776); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver(42, 0.01785967399007796); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
source_py: def probability_three_randomly_chosen_numbers_ap(n):
      return ((3.0 * n) / ((4.0 * (n * n)) - 1))
source_cpp: double probability_three_randomly_chosen_numbers_ap(int n) {
    return ( 3.0 * n ) / ( 4.0 * ( n * n ) - 1 );
  }