Uva 11181 Solution

Solution : Probability|Given

This problem is related to conditional probability. 

This problem given n people and the probability of each person will shop and also given r that is r person will shop and the rest will not shop. 

# P(B) = Probability of B.

Conditional Probability : Suppose A and B are two event. A event depend on B event and A event occur after the B event. We can write this P(A | B) and its means A event occur after the B event occur.

Now according to Conditional Probability we can write this, 

    

                              P(A | B) = ^{P(A ∩ B)} / _P(B)

 

                                           = ^{n(A ∩ B)} / _n(B)

update comming.....................

#include<bits/stdc++.h>

using namespace std;

double prob[50], total[50], n, r;

double Count(int pos, int k, double p)

{

    if(pos == n)

    {

        if(k == r)

            return p;

        else

            return 0;

    }

    double r1 = 0, r2 = 0;

    r1 = Count( pos+1, k, p*(1 - prob[pos]) );

    if(k < r)

    {

        r2 = Count( pos+1, k+1, p*prob[pos] );

        total[pos] += r2;

    }

    return r1+r2;

}

int main()

{

    int j = 1;

    while(cin >> n >> r)

    {

        if(n == 0 && r == 0)

            break;

        for(int i=0; i<n; i++)

        {

            cin >> prob[i];

            total[i] = 0;

        }

        double total_probability = Count(0, 0, 1);

        cout << showpoint;

        cout << fixed;

        cout << setprecision(6);

        cout << "Case " << j++ << ":\n";

        for(int i=0; i<n; i++)

            cout << total[i]/total_probability << "\n";

    }

    return 0;

}