Probability of A winning the match when individual probabilities of hitting the target given
Last Updated :
22 Jun, 2022
Given four integers a, b, c and d. Player A & B try to score a penalty. Probability of A shooting the target is a / b while probability of B shooting the target is c / d. The player who scores the penalty first wins. The task is to find the probability of A winning the match.
Examples:
Input: a = 1, b = 3, c = 1, d = 3
Output: 0.6
Input: a = 1, b = 2, c = 10, d = 11
Output: 0.52381
Approach: If we consider variables K = a / b as the probability of A shooting the target and R = (1 – (a / b)) * (1 – (c / d)) as the probability that A as well as B both missing the target.
Therefore, the solution forms a Geometric progression K * R0 + K * R1 + K * R2 + ….. whose sum is (K / 1 – R). After putting the values of K and R we get the formula as K * (1 / (1 – (1 – r) * (1 – k))).
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
double getProbability( int a, int b, int c, int d)
{
double p = ( double )a / ( double )b;
double q = ( double )c / ( double )d;
double ans = p * (1 / (1 - (1 - q) * (1 - p)));
return ans;
}
int main()
{
int a = 1, b = 2, c = 10, d = 11;
cout << getProbability(a, b, c, d);
return 0;
}
|
Java
class GFG
{
static double getProbability( int a, int b,
int c, int d)
{
double p = ( double ) a / ( double ) b;
double q = ( double ) c / ( double ) d;
double ans = p * ( 1 / ( 1 - ( 1 - q) *
( 1 - p)));
return ans;
}
public static void main(String[] args)
{
int a = 1 , b = 2 , c = 10 , d = 11 ;
System.out.printf( "%.5f" ,
getProbability(a, b, c, d));
}
}
|
Python3
def getProbability(a, b, c, d) :
p = a / b;
q = c / d;
ans = p * ( 1 / ( 1 - ( 1 - q) * ( 1 - p)));
return round (ans, 5 );
if __name__ = = "__main__" :
a = 1 ; b = 2 ; c = 10 ; d = 11 ;
print (getProbability(a, b, c, d));
|
C#
using System;
class GFG
{
public static double getProbability( int a, int b,
int c, int d)
{
double p = ( double ) a / ( double ) b;
double q = ( double ) c / ( double ) d;
double ans = p * (1 / (1 - (1 - q) *
(1 - p)));
return ans;
}
public static void Main( string [] args)
{
int a = 1, b = 2, c = 10, d = 11;
Console.Write( "{0:F5}" ,
getProbability(a, b, c, d));
}
}
|
PHP
<?php
function getProbability( $a , $b , $c , $d )
{
$p = $a / $b ;
$q = $c / $d ;
$ans = $p * (1 / (1 - (1 - $q ) * (1 - $p )));
return round ( $ans ,6);
}
$a = 1;
$b = 2;
$c = 10;
$d = 11;
echo getProbability( $a , $b , $c , $d );
?>
|
Javascript
<script>
function getProbability(a , b , c , d) {
var p = a / b;
var q = c / d;
var ans = p * (1 / (1 - (1 - q) * (1 - p)));
return ans;
}
var a = 1, b = 2, c = 10, d = 11;
document.write( getProbability(a, b, c, d).toFixed(5));
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
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