# Probability of getting more value in third dice throw

Given that the three players playing a game of rolling a dice. Player1 rolled a dice got A and player2 rolled a dice got B. The task is to find the probability of player3 to win the match and Player3 wins if he gets more than both of them.

Examples:

```Input: A = 2, B = 3
Output: 1/2
Player3 wins if he gets 4 or 5 or 6

Input: A = 1, B = 2
Output: 2/3
Player3 wins if he gets 3 or 4 or 5 or 6
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to find the maximum of A and B and then 6-max(A, B) gives us remaining numbers C should get to win the match. So, one can find the answer dividing 6-max(A, B) and 6 with GCD of these two.

## C++

 `// CPP program to find probability to C win the match ` `#include ` `using` `namespace` `std; ` ` `  `// function to find probability to C win the match ` `void` `Probability(``int` `A, ``int` `B) ` `{ ` `    ``int` `C = 6 - max(A, B); ` ` `  `    ``int` `gcd = __gcd(C, 6); ` ` `  `    ``cout << C / gcd << ``"/"` `<< 6 / gcd; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `A = 2, B = 4; ` ` `  `    ``// function call ` `    ``Probability(A, B); ` ` `  `    ``return` `0; ` `} `

## Java

 `//  Java program to find probability to C win the match ` ` `  `import` `java.io.*; ` ` `  `class` `GFG {``// Recursive function to return gcd of a and b  ` `    ``static` `int` `__gcd(``int` `a, ``int` `b)  ` `    ``{  ` `        ``// Everything divides 0   ` `        ``if` `(a == ``0``)  ` `          ``return` `b;  ` `        ``if` `(b == ``0``)  ` `          ``return` `a;  ` `        `  `        ``// base case  ` `        ``if` `(a == b)  ` `            ``return` `a;  ` `        `  `        ``// a is greater  ` `        ``if` `(a > b)  ` `            ``return` `__gcd(a-b, b);  ` `        ``return` `__gcd(a, b-a);  ` `    ``} ` `     `  `   `  `// function to find probability to C win the match ` `static` `void` `Probability(``int` `A, ``int` `B) ` `{ ` `    ``int` `C = ``6` `- Math.max(A, B); ` ` `  `    ``int` `gcd = __gcd(C, ``6``); ` ` `  `    ``System.out.print( C / gcd + ``"/"` `+ ``6` `/ gcd); ` `} ` ` `  `// Driver code ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `    ``int` `A = ``2``, B = ``4``; ` ` `  `    ``// function call ` `    ``Probability(A, B); ` `    ``} ` `} ` `// This code is contributed by shs.. `

## Python 3

 `# Python 3 program to find probability ` `# to C win the match ` ` `  `# import gcd() from math lib. ` `from` `math ``import` `gcd ` ` `  `# function to find probability  ` `# to C win the match ` `def` `Probability(A, B) : ` `    ``C ``=` `6` `-` `max``(A, B) ` `     `  `    ``__gcd ``=` `gcd(C, ``6``) ` `     `  `    ``print``(C ``/``/` `__gcd, ``"/"``, ``6` `/``/` `__gcd) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``A, B ``=` `2``, ``4` ` `  `    ``# function call ` `    ``Probability(A, B) ` `     `  `# This code is contributed by ANKITRAI1 `

## C#

 `// C# program to find probability  ` `// to C win the match  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Recursive function to return  ` `// gcd of a and b  ` `static` `int` `__gcd(``int` `a, ``int` `b)  ` `{  ` `    ``// Everything divides 0  ` `    ``if` `(a == 0)  ` `        ``return` `b;  ` `    ``if` `(b == 0)  ` `        ``return` `a;  ` `     `  `    ``// base case  ` `    ``if` `(a == b)  ` `        ``return` `a;  ` `     `  `    ``// a is greater  ` `    ``if` `(a > b)  ` `        ``return` `__gcd(a - b, b);  ` `    ``return` `__gcd(a, b - a);  ` `}  ` ` `  `// function to find probability  ` `// to C win the match  ` `static` `void` `Probability(``int` `A, ``int` `B)  ` `{  ` `    ``int` `C = 6 - Math.Max(A, B);  ` ` `  `    ``int` `gcd = __gcd(C, 6);  ` ` `  `    ``Console.Write(C / gcd + ``"/"` `+ 6 / gcd);  ` `}  ` ` `  `// Driver code  ` `static` `public` `void` `Main () ` `{ ` `    ``int` `A = 2, B = 4;  ` `     `  `    ``// function call  ` `    ``Probability(A, B);  ` `}  ` `}  ` ` `  `// This code is contributed by ajit.  `

## PHP

 ` `

Output:

```1/3
``` My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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