# 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 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 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 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. *

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

`#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; ` `} ` |

*chevron_right*

*filter_none*

References:

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

This article is compiled by **Shashank Sinha** and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

## Recommended Posts:

- Coin Change | DP-7
- Frobenius coin problem
- Expected number of coin flips to get two heads in a row?
- Probability of getting two consecutive heads after choosing a random coin among two different types of coins
- Make all numbers of an array equal
- Minimum removals to make array sum odd
- Minimum multiplications with {2, 3, 7} to make two numbers equal
- Minimum removals from array to make GCD greater
- Minimum number of changes required to make the given array an AP
- Minimum operations to make GCD of array a multiple of k
- Minimum gcd operations to make all array elements one
- Find minimum number of coins that make a given value
- Make all elements of an array equal with the given operation
- Possible to make a divisible by 3 number using all digits in an array
- Minimum number of given moves required to make N divisible by 25