# Make a fair coin from a biased coin

You are given a function foo() that represents a biased coin. When foo() is called, it returns 0 with 60% probability, and 1 with 40% probability. Write a new function that returns 0 and 1 with a 50% probability each. Your function should use only foo(), no other library method.

**Solution:**

We know foo() returns 0 with 60% probability. How can we ensure that 0 and 1 are returned with a 50% probability?

The solution is similar to this post. If we can somehow get two cases with equal probability, then we are done. We call foo() two times. Both calls will return 0 with a 60% probability. So the two pairs (0, 1) and (1, 0) will be generated with equal probability from two calls of foo(). Let us see how.**(0, 1):** The probability to get 0 followed by 1 from two calls of foo() = 0.6 * 0.4 = 0.24 **(1, 0):** The probability to get 1 followed by 0 from two calls of foo() = 0.4 * 0.6 = 0.24*So the two cases appear with equal probability. The idea is to return consider only the above two cases, return 0 in one case, return 1 in other case. For other cases [(0, 0) and (1, 1)], recur until you end up in any of the above two cases. *

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The below program depicts how we can use foo() to return 0 and 1 with equal probability.

## C++

`#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `foo() ` `// given method that returns 0` ` ` `// with 60% probability and 1 with 40%` `{` ` ` `// some code here` `}` `// returns both 0 and 1 with 50% probability` `int` `my_fun()` `{` ` ` `int` `val1 = foo();` ` ` `int` `val2 = foo();` ` ` `if` `(val1 == 0 && val2 == 1)` ` ` `return` `0; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `if` `(val1 == 1 && val2 == 0)` ` ` `return` `1; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `return` `my_fun(); ` `// will reach here with` ` ` `// (1 - 0.24 - 0.24) probability` `}` `// Driver Code` `int` `main()` `{` ` ` `cout << my_fun();` ` ` `return` `0;` `}` `// This is code is contributed` `// by rathbhupendra` |

## C

`#include <stdio.h>` `int` `foo() ` `// given method that returns 0 with 60%` ` ` `// probability and 1 with 40%` `{` ` ` `// some code here` `}` `// returns both 0 and 1 with 50% probability` `int` `my_fun()` `{` ` ` `int` `val1 = foo();` ` ` `int` `val2 = foo();` ` ` `if` `(val1 == 0 && val2 == 1)` ` ` `return` `0; ` `// Will reach here with 0.24 probability` ` ` `if` `(val1 == 1 && val2 == 0)` ` ` `return` `1; ` `// // Will reach here with 0.24` ` ` `// probability` ` ` `return` `my_fun(); ` `// will reach here with (1 - 0.24 -` ` ` `// 0.24) probability` `}` `int` `main()` `{` ` ` `printf` `(` `"%d "` `, my_fun());` ` ` `return` `0;` `}` |

## Java

`import` `java.io.*;` `class` `GFG {` ` ` `// Given method that returns 0` ` ` `// with 60% probability and 1 with 40%` ` ` `static` `int` `foo()` ` ` `{` ` ` `// some code here` ` ` `}` ` ` `// Returns both 0 and 1 with 50% probability` ` ` `static` `int` `my_fun()` ` ` `{` ` ` `int` `val1 = foo();` ` ` `int` `val2 = foo();` ` ` `if` `(val1 == ` `0` `&& val2 == ` `1` `)` ` ` `return` `0` `; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `if` `(val1 == ` `1` `&& val2 == ` `0` `)` ` ` `return` `1` `; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `return` `my_fun(); ` `// will reach here with` ` ` `// (1 - 0.24 - 0.24) probability` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `System.out.println(my_fun());` ` ` `}` `}` `// This code is contributed by ShubhamCoder` |

## Python3

`# Python3 program for the` `# above approach` `def` `foo():` ` ` ` ` `# Some code here` ` ` `pass` `# Returns both 0 and 1` `# with 50% probability` `def` `my_fun():` ` ` ` ` `val1, val2 ` `=` `foo(), foo()` ` ` ` ` `if` `val1 ^ val2:` ` ` ` ` `# Will reach here with` ` ` `# (0.24 + 0.24) probability` ` ` `return` `val1` ` ` ` ` `# Will reach here with` ` ` `# (1 - 0.24 - 0.24) probability` ` ` `return` `my_fun()` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `print` `(my_fun())` `# This code is contributed by sgshah2` |

## C#

`using` `System;` `class` `GFG {` ` ` `// given method that returns 0` ` ` `// with 60% probability and 1 with 40%` ` ` `static` `int` `foo()` ` ` `{` ` ` `// some code here` ` ` `}` ` ` `// returns both 0 and 1 with 50% probability` ` ` `static` `int` `my_fun()` ` ` `{` ` ` `int` `val1 = foo();` ` ` `int` `val2 = foo();` ` ` `if` `(val1 == 0 && val2 == 1)` ` ` `return` `0; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `if` `(val1 == 1 && val2 == 0)` ` ` `return` `1; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `return` `my_fun(); ` `// will reach here with` ` ` `// (1 - 0.24 - 0.24) probability` ` ` `}` ` ` `// Driver Code` ` ` `static` `public` `void` `Main() { Console.Write(my_fun()); }` `}` `// This is code is contributed` `// by ShubhamCoder` |

## PHP

`<?php` `function` `foo() ` `// given method that returns 0` ` ` `// with 60% probability and 1 with 40%` `{` ` ` `// some code here` `}` `// returns both 0 and 1 with 50% probability` `function` `my_fun()` `{` ` ` `$val1` `= foo();` ` ` `$val2` `= foo();` ` ` `if` `(` `$val1` `== 0 && ` `$val2` `== 1)` ` ` `return` `0; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `if` `(` `$val1` `== 1 && ` `$val2` `== 0)` ` ` `return` `1; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` `return` `my_fun(); ` `// will reach here with` ` ` `// (1 - 0.24 - 0.24) probability` `}` `// Driver Code` `echo` `my_fun();` `// This is code is contributed` `// by Akanksha Rai` `?>` |

## Javascript

`<script>` `// Given method that returns 0 with` `// 60% probability and 1 with 40%` `function` `foo()` `{` ` ` `// Some code here` `}` `// Returns both 0 and 1 with` `// 50% probability` `function` `my_fun()` `{` ` ` `var` `val1 = foo();` ` ` `var` `val2 = foo();` ` ` ` ` `if` `(val1 == 0 && val2 == 1)` ` ` `return` `0; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` ` ` `if` `(val1 == 1 && val2 == 0)` ` ` `return` `1; ` `// Will reach here with` ` ` `// 0.24 probability` ` ` ` ` `return` `my_fun(); ` `// Will reach here with` ` ` `// (1 - 0.24 - 0.24) probability` `}` `// Driver Code` `document.write(my_fun());` `// This code is contributed by noob2000` `</script>` |

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

References:

http://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_biased_coin

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