Probabilidad de que A gane el partido cuando se dan las probabilidades individuales de dar en el blanco

Dados cuatro enteros a , b , c y d . Los jugadores A y B intentan marcar un penalti. La probabilidad de que A dispare al blanco es a/b mientras que la probabilidad de que B dispare al blanco es c/d . Gana el jugador que primero marca el penalti. La tarea es encontrar la probabilidad de que A gane el partido.
Ejemplos: 
 

Entrada: a = 1, b = 3, c = 1, d = 3 
Salida: 0,6
Entrada: a = 1, b = 2, c = 10, d = 11 
Salida: 0,52381 
 

Planteamiento: Si consideramos las variables K = a/b como la probabilidad de que A dispare al blanco y R = (1 – (a/b)) * (1 – (c/d)) como la probabilidad de que tanto A como B ambos fallando el objetivo. 
Por tanto, la solución forma una progresión Geométrica K * R ⁰ + K * R ¹ + K * R ² + ….. cuya suma es (K / 1 – R) . Después de poner los valores de K y R obtenemos la fórmula como K * (1 / (1 – (1 – r) * (1 – k))) .
A continuación se muestra la implementación del enfoque anterior: 
 

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the probability of A winning
double getProbability(int a, int b, int c, int d)
{
 
    // p and q store the values
    // of fractions a / b and c / d
    double p = (double)a / (double)b;
    double q = (double)c / (double)d;
 
    // To store the winning probability of A
    double ans = p * (1 / (1 - (1 - q) * (1 - p)));
    return ans;
}
 
// Driver code
int main()
{
    int a = 1, b = 2, c = 10, d = 11;
    cout << getProbability(a, b, c, d);
 
    return 0;
}

// Java implementation of the approach
class GFG
{
 
// Function to return the probability
// of A winning
static double getProbability(int a, int b,
                             int c, int d)
{
 
    // p and q store the values
    // of fractions a / b and c / d
    double p = (double) a / (double) b;
    double q = (double) c / (double) d;
 
    // To store the winning probability of A
    double ans = p * (1 / (1 - (1 - q) *
                               (1 - p)));
    return ans;
}
 
// Driver code
public static void main(String[] args)
{
    int a = 1, b = 2, c = 10, d = 11;
    System.out.printf("%.5f",
               getProbability(a, b, c, d));
}
}
 
// This code contributed by Rajput-Ji

# Python3 implementation of the approach
 
# Function to return the probability
# of A winning
def getProbability(a, b, c, d) :
 
    # p and q store the values
    # of fractions a / b and c / d
    p = a / b;
    q = c / d;
     
    # To store the winning probability of A
    ans = p * (1 / (1 - (1 - q) * (1 - p)));
     
    return round(ans,5);
 
# Driver code
if __name__ == "__main__" :
 
    a = 1; b = 2; c = 10; d = 11;
    print(getProbability(a, b, c, d));
 
# This code is contributed by Ryuga

// C# implementation of the approach
using System;
 
class GFG
{
 
// Function to return the probability
// of A winning
public static double getProbability(int a, int b,
                                    int c, int d)
{
 
    // p and q store the values
    // of fractions a / b and c / d
    double p = (double) a / (double) b;
    double q = (double) c / (double) d;
 
    // To store the winning probability of A
    double ans = p * (1 / (1 - (1 - q) *
                               (1 - p)));
    return ans;
}
 
// Driver code
public static void Main(string[] args)
{
    int a = 1, b = 2, c = 10, d = 11;
    Console.Write("{0:F5}",
                   getProbability(a, b, c, d));
}
}
 
// This code is contributed by Shrikant13

<?php
// PHP implementation of the approach
 
// Function to return the probability
// of A winning
function getProbability($a, $b, $c, $d)
{
 
    // p and q store the values
    // of fractions a / b and c / d
    $p = $a / $b;
    $q = $c / $d;
 
    // To store the winning probability of A
    $ans = $p * (1 / (1 - (1 - $q) * (1 - $p)));
    return round($ans,6);
}
 
// Driver code
$a = 1;
$b = 2;
$c = 10;
$d = 11;
echo getProbability($a, $b, $c, $d);
 
// This code is contributed by chandan_jnu
?>

<script>
 
// JavaScript implementation of the approach   
 
// Function to return the probability
// of A winning
    function getProbability(a , b , c , d) {
 
        // p and q store the values
        // of fractions a / b and c / d
        var p =  a /  b;
        var q =  c /  d;
 
        // To store the winning probability of A
        var ans = p * (1 / (1 - (1 - q) * (1 - p)));
        return ans;
    }
 
    // Driver code
     
        var a = 1, b = 2, c = 10, d = 11;
        document.write( getProbability(a, b, c, d).toFixed(5));
 
// This code contributed by aashish1995
 
</script>

0.52381

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Espacio Auxiliar: O(1)