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# Probability of getting more value in third dice throw

• Difficulty Level : Medium
• Last Updated : 11 Jul, 2022

Given that the three players playing a game of rolling dice. Player1 rolled a die got A and player2 rolled a die 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 ```

Approach: The idea is to find the maximum of A and B and then 6-max(A, B) gives us the 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

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## Javascript

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Output:

`1/3`

Time Complexity: O(log(min(a, b))), where a and b are two parameters of gcd.

Auxiliary Space: O(log(min(a, b)))

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