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

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 the rand50() method. Also, the 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 the above idea :

## 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`

## Python3

 `# Program to print 1 with 75% probability and 0` `# with 25% probability` `from` `random ``import` `randrange`   `# Random Function to that returns 0 or 1 with` `# equal probability` `def` `rand50():` `  `  `        ``# The randrange function will generate integer` `    ``# between the half closed interval at end` `    ``# Here by passing parameter as 0,2` `    ``# the function will generate integer between 0 and 1` `    ``return` `(``int``)(randrange(``0``, ``2``)) & ``1`   `# Random Function to that returns 1 with 75%` `# probability and 0 with 25% probability using` `# Bitwise OR` `def` `rand75():` `    ``return` `rand50() | rand50()`   `# Driver code to test above functions` `for` `i ``in` `range``(``0``, ``50``):` `    ``print``(rand75(), end``=``"")`   `    ``# This code is contributed by meetgor.`

## C#

 `// C# program to print 1 with 75% probability and 0 ` `// with 25% probability `     `using` `System;`   `public` `class` `GFG` `{` `    ``// Instantiate random number generator` `    ``static` `Random rand = ``new` `Random();` `    `  `    ``// Random Function to that returns 0 or 1 with ` `    ``// equal probability ` `    ``static` `int` `rand50()` `    ``{`   `        `  `        ``// rand() function will generate 1 or 0 ` `        ``// with equal probability` `        ``return` `rand.Next(0, 2);` `    ``}`   `    ``// Random Function to that returns 1 with 75% ` `    ``// probability and 0 with 25% probability using ` `    ``// Bitwise OR ` `    ``static` `int` `rand75()` `    ``{` `        ``return` `rand50() | rand50();` `    ``}` `    ``public` `static` `void` `Main(``string``[] args)` `    ``{`     `        ``for` `(``int` `i = 0; i < 50; i++)` `        ``{` `            ``Console.Write(rand75());` `        ``}` `    ``}` `}`   `//this code is contributed by phasing17`

## PHP

 ``

## Javascript

 ``

Output

`11101010110101011010000101011110100010111110101111`

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());
}```

Below is the implementation of the above idea :

## C++

 `#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 AND` `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

 `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 AND` `    ``static` `int` `rand75()` `    ``{` `        ``return` `(rand50() & rand50())^``1``;` `    ``}` ` `  `    ``// 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());` `        ``}` ` `  `    ``}` ` `  `}`

## Python3

 `from` `random ``import` `randrange` ` `  `# Random Function to that returns 0 or 1 with` `# equal probability` `def` `rand50():` `  ``return` `((``int``)(randrange(``0``, ``2``)) & ``1``)` `  `    `def` `rand75():` `  ``return` `(rand50() & rand50())^``1` ` `    `for` `i ``in` `range``(``0``, ``50``):` `    ``print``(rand75(), end``=``"")`

## C#

 `// C# program to implement the approach` `using` `System;`   `class` `GFG ` `{`   `  ``// Random Function to that returns 0 or 1 with` `  ``// equal probability` `  ``static` `int` `rand50()` `  ``{`   `    ``// Instantiate random number generator using` `    ``// system-supplied value as seed.` `    ``var` `rand = ``new` `Random();`   `    ``// rand() function will generate 0 or 1` `    ``// number with equal probability.` `    ``return` `rand.Next(0, 2);` `  ``}`   `  ``// Random Function to that returns 1 with 75%` `  ``// probability and 0 with 25% probability using` `  ``// Bitwise AND` `  ``static` `int` `rand75()` `  ``{` `    ``return` `(rand50() & rand50()) ^ 1;` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `Main(``string``[] args)` `  ``{` `    `  `    ``// Initialize random number generator` `    ``// srand(time(null));` `    ``for` `(``int` `i = 0; i < 50; i++) {` `      ``Console.Write(rand75());` `    ``}` `  ``}` `}`   `// This code is contributed by phasing17`

## Javascript

 `// JavaScript program to implement the approach`   `// Random Function to that returns 0 or 1 with` `// equal probability` `function` `rand50()` `{` `  ``return` `(Math.floor(Math.random() * 2) & 1);` `}  `   `function` `rand75()` `{` `  ``return` `(rand50() & rand50())^1;` `}` ` `    `for` `(``var` `i = 0; i < 50; i++)` `    ``process.stdout.write(rand75().toString());` `    `  `    `  `//This code is contributed by phasing17`

Output

`11111111000111101111110011111110011110111111010111`

We can replace Bitwise OR and Bitwise AND operators with 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 the 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`

## Python3

 `# Program to print 1 with 75% probability and 0` `# with 25% probability` `from` `random ``import` `randrange`   `# Random Function to that returns 0 or 1 with` `# equal probability` `def` `rand50():` `        ``# rand range function generates a integer between` `    ``# the provided ranges which is half closed interval` `    ``# It will generate integer 0 or 1 if passed 0,2 as parameter` `    ``return` `(``int``)(randrange(``0``, ``2``)) & ``1`   `# Random Function to that returns 1 with 75%` `# probability and 0 with 25% probability using` `# left shift and Bitwise XOR`     `def` `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` `1` `if` `(x > ``0``) ``else` `0`   `# Driver code to test above functions` `for` `i ``in` `range``(``0``, ``50``):` `    ``print``(rand75(), end``=``"")`   `    ``# This code is contributed by meetgor.`

## C#

 `// C# program to print 1 with 75% probability and 0` `// with 25% probability` `using` `System;` `public` `class` `GFG` `{` `    `  `    ``// Random Function to that returns 0 or 1 with` `    ``// equal probability` `    ``static` `Random rnd = ``new` `Random();` `    ``static` `int` `rand50()` `    ``{` `      `  `        ``// Next(2) will generate 0 or 1 with equal probability` `        ``return` `rnd.Next(2);` `    ``}` `     `  `    ``// 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;` `    ``}` `    `  `    ``static` `public` `void` `Main (){` `        ``for` `(``int` `i = 0; i < 50; i++)` `            ``Console.Write(rand75());` `    ``}` `}`   `// This code is contributed by shruti456rawal`

## 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

`10110100111011011110111100101111110111100001111111`

Time Complexity: O(1)
Auxiliary Space: O(1)

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