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# Generate 0 and 1 with 25% and 75% probability

• Difficulty Level : Medium
• Last Updated : 14 Jun, 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 :

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## C++

 `// Program to print 1 with 75% probability and 0``// with 25% probability``#include ``using` `namespace` `std;` `// Random Function to that returns 0 or 1 with``// equal probability``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` `rand``() & 1;``}` `// Random Function to that returns 1 with 75%``// probability and 0 with 25% probability using``// Bitwise OR``bool` `rand75()``{``    ``return` `rand50() | rand50();``}` `// Driver code to test above functions``int` `main()``{``    ``// Initialize random number generator``    ``srand``(``time``(NULL));` `    ``for``(``int` `i = 0; i < 50; i++)``        ``cout << rand75();` `    ``return` `0;``}`

## Java

 `// Java program to print 1 with 75% probability and 0``// with 25% probability``class` `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

 ``

## Javascript

 ``

Output:

`11101111110010010110011111111101111110111100011000`

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++

 `// Program to print 1 with 75% probability and 0``// with 25% probability``#include ``using` `namespace` `std;` `// Random Function to that returns 0 or 1 with``// equal probability``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` `rand``() & 1;``}` `// Random Function to that returns 1 with 75%``// probability and 0 with 25% probability using``// left shift and Bitwise XOR``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 code to test above functions``int` `main()``{``    ``// Initialize random number generator``    ``srand``(``time``(NULL));` `    ``for` `(``int` `i = 0; i < 50; i++)``        ``cout << rand75();` `    ``return` `0;``}`

## Java

 `// Java program to print 1 with 75% probability and 0``// with 25% probability``class` `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``// left shift and Bitwise XOR``static` `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 code``public` `static` `void` `main(String[] args)``{` `    ``for` `(``int` `i = ``0``; i < ``50``; i++)``        ``System.out.print(rand75());``}``}` `// This code is contributed by 29AjayKumar`

## PHP

 ` 0) ? 1 : 0;``}` `// Driver code` `// Initialize random``// number generator``srand(time(NULL));` `for` `(``\$i` `= 0; ``\$i` `< 50; ``\$i``++)``    ``echo` `rand75();``    ` `// This code is contributed``// by ajit``?>`

## Javascript

 ``

Output:

`01101110111011000111111111110001111011101110110110`

Please note above solutions will produce different results every time we run them.