Generate 0 and 1 with 25% and 75% probability - GeeksforGeeks

06 Nov, 2021
Given a function rand50() that returns 0 or 1 with equal probability, write a function that returns 1 with 75% probability and 0 with 25% probability using rand50() only. Minimize the number of calls to rand50() method. Also, use of any other library function and floating point arithmetic are not allowed. 
The idea is to use Bitwise OR. A bitwise OR takes two bits and returns 0 if both bits are 0, while otherwise the result is 1. So it has 75% probability that it will return 1.Below is the implementation of above idea : 
C++
Java
PHP
Javascript
// Program to print 1 with 75% probability and 0// with 25% probability#include <iostream>using namespace std; // Random Function to that returns 0 or 1 with// equal probabilityint rand50(){    // rand() function will generate odd or even    // number with equal probability. If rand()    // generates odd number, the function will    // return 1 else it will return 0.    return rand() & 1;} // Random Function to that returns 1 with 75%// probability and 0 with 25% probability using// Bitwise ORbool rand75(){    return rand50() | rand50();} // Driver code to test above functionsint main(){    // Initialize random number generator    srand(time(NULL));     for(int i = 0; i < 50; i++)        cout << rand75();     return 0;}
// Java program to print 1 with 75% probability and 0// with 25% probabilityclass GFG{     // Random Function to that returns 0 or 1 with    // equal probability    static int rand50()    {        // rand() function will generate odd or even        // number with equal probability. If rand()        // generates odd number, the function will        // return 1 else it will return 0.        return (int) (10 * Math.random()) & 1;    }     // Random Function to that returns 1 with 75%    // probability and 0 with 25% probability using    // Bitwise OR    static int rand75()    {        return rand50() | rand50();    }     // Driver code    public static void main(String[] args)    {        // Initialize random number generator        //srand(time(null));         for (int i = 0; i < 50; i++)        {            System.out.print(rand75());        }     } } // This code is contributed by 29AjayKumar
<?php// Program to print 1 with 75% probability// and 0 with 25% probability // Random Function to that returns 0 or// 1 with equal probabilityfunction rand50(){         // rand() function will generate    // odd or even number with equal    // probability. If rand() generates    // odd number, the function will    // return 1 else it will return 0.    return rand() & 1;} // Random Function to that returns// 1 with 75% probability and 0// with 25% probability using// Bitwise ORfunction rand75(){    return rand50() | rand50();}     // Driver Code    // Initialize random    // number generator    srand(time(NULL));     for($i = 0; $i < 50; $i++)        echo rand75(); // This code is contributed m_kit?>
<script>// Program to print 1 with 75% probability and 0// with 25% probability  // Random Function to that returns 0 or 1 with// equal probabilityfunction rand50() {    // rand() function will generate odd or even    // number with equal probability. If rand()    // generates odd number, the function will    // return 1 else it will return 0.    return Math.floor(Math.random() * 10) & 1;} // Random Function to that returns 1 with 75%// probability and 0 with 25% probability using// Bitwise ORfunction rand75() {    return rand50() | rand50();} // Driver code to test above functions // Initialize random number generator  for (let i = 0; i < 50; i++)    document.write(rand75());   // This code is contributed by gfgking</script>
Output:  
11101111110010010110011111111101111110111100011000
Time Complexity: O(1)
Auxiliary Space: O(1)
On similar lines, we can also use Bitwise AND. Since it returns 0 with 75% probability, we have to invert the result. 
// Random Function to that returns 1 with 75% 
// probability and 0 with 25% probability using
// Bitwise AND
bool rand75() 
{
    return !(rand50() & rand50());
}
We can replace Bitwise OR and Bitwise AND operator by OR and AND operators as well –  
// Random Function to that returns 1 with 75%
// probability and 0 with 25% probability using 
// OR or AND operator
int rand75()
{
    return !(rand50() && rand50());
    // return rand50() || rand50()
}
We can also achieve the result using left shift operator and Bitwise XOR –  
C++
Java
PHP
Javascript
// Program to print 1 with 75% probability and 0// with 25% probability#include <iostream>using namespace std; // Random Function to that returns 0 or 1 with// equal probabilityint rand50(){    // rand() function will generate odd or even    // number with equal probability. If rand()    // generates odd number, the function will    // return 1 else it will return 0.    return rand() & 1;} // Random Function to that returns 1 with 75%// probability and 0 with 25% probability using// left shift and Bitwise XORint rand75(){    // x is one of {0, 1}    int x = rand50();     x = x << 1;     // x is now one of {00, 10}     x = x ^ rand50();     // x is now one of {00, 01, 10, 11}     return (x > 0) ? 1 : 0;} // Driver code to test above functionsint main(){    // Initialize random number generator    srand(time(NULL));     for (int i = 0; i < 50; i++)        cout << rand75();     return 0;}
// Java program to print 1 with 75% probability and 0// with 25% probabilityclass GFG{ // Random Function to that returns 0 or 1 with// equal probabilitystatic int rand50(){    // rand() function will generate odd or even    // number with equal probability. If rand()    // generates odd number, the function will    // return 1 else it will return 0.    return (int) (10 * Math.random()) & 1;} // Random Function to that returns 1 with 75%// probability and 0 with 25% probability using// left shift and Bitwise XORstatic int rand75(){    // x is one of {0, 1}    int x = rand50();     x = x << 1;     // x is now one of {00, 10}     x = x ^ rand50();     // x is now one of {00, 01, 10, 11}     return (x > 0) ? 1 : 0;} // Driver codepublic static void main(String[] args){     for (int i = 0; i < 50; i++)        System.out.print(rand75());}} // This code is contributed by 29AjayKumar
<?php// Program to print 1 with// 75% probability and 0// with 25% probability // Random Function to that// returns 0 or 1 with// equal probabilityfunction rand50(){    // rand() function will    // generate odd or even    // number with equal    // probability. If rand()    // generates odd number,    // the function will return    // 1 else it will return 0.    return rand() & 1;} // Random Function to that// returns 1 with 75%// probability and 0 with// 25% probability using// left shift and Bitwise XORfunction rand75(){    // x is one of {0, 1}    $x = rand50();     $x = $x << 1;     // x is now one    // of {00, 10}     $x = $x ^ rand50();     // x is now one of    // {00, 01, 10, 11}     return ($x > 0) ? 1 : 0;} // Driver code // Initialize random// number generatorsrand(time(NULL)); for ($i = 0; $i < 50; $i++)    echo rand75();     // This code is contributed// by ajit?>
<script>// Javascript program to print 1 with 75% probability and 0// with 25% probability     // Random Function to that returns 0 or 1 with    // equal probabilityfunction rand50(){         // rand() function will generate odd or even        // number with equal probability. If rand()        // generates odd number, the function will        // return 1 else it will return 0.        return  Math.floor((10 * Math.random())) & 1;}     // Random Function to that returns 1 with 75%    // probability and 0 with 25% probability using    // Bitwise ORfunction rand75(){    // x is one of {0, 1}    let x = rand50();      x = x << 1;      // x is now one of {00, 10}      x = x ^ rand50();      // x is now one of {00, 01, 10, 11}      return (x > 0) ? 1 : 0;} // Driver code  for (let i = 0; i < 50; i++){    document.write(rand75());} // This code is contributed by rag2127</script>
Output:  
01101110111011000111111111110001111011101110110110
Time Complexity: O(1)
Auxiliary Space: O(1)
Please note above solutions will produce different results every time we run them.This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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