# Probability of getting more value in third dice throw

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 = 3Output:1/2 Player3 wins if he gets 4 or 5 or 6Input:A = 1, B = 2Output: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 <bits/stdc++.h>` `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

`<?php` `// PHP program to find probability` `// to C win the match` `// Find gcd()` `function` `__gcd(` `$a` `, ` `$b` `)` `{` ` ` `if` `(` `$b` `== 0)` ` ` `return` `$a` `;` ` ` `return` `__gcd(` `$b` `, ` `$a` `% ` `$b` `);` `}` `// function to find probability` `// to C win the match` `function` `Probability(` `$A` `, ` `$B` `)` `{` ` ` `$C` `= 6 - max(` `$A` `, ` `$B` `);` ` ` `$gcd` `= __gcd(` `$C` `, 6);` ` ` `echo` `(` `$C` `/ ` `$gcd` `) . ` `"/"` `.` ` ` `(6 / ` `$gcd` `);` `}` `// Driver code` `$A` `= 2;` `$B` `= 4;` `// function call` `Probability(` `$A` `, ` `$B` `);` `// This code is contributed by mits` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to find probability` ` ` `// to C win the match` ` ` ` ` `// Recursive function to return` ` ` `// gcd of a and b` ` ` `function` `__gcd(a, 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` ` ` `function` `Probability(A, B)` ` ` `{` ` ` `let C = 6 - Math.max(A, B);` ` ` `let gcd = __gcd(C, 6);` ` ` `document.write(parseInt(C / gcd, 10) + ` `"/"` `+ parseInt(6 / gcd, 10));` ` ` `}` ` ` ` ` `let A = 2, B = 4;` ` ` ` ` `// function call` ` ` `Probability(A, B);` ` ` `</script>` |

**Output:**

1/3