// Sonny's solution to dice
// Stanford Local Programming Contest, October 2007

#include <iostream>
#include <iomanip>

using namespace std;

const int digits = 5;
const double sentry = -1.0;

int dice[51];
double P[51][1001];

// recursive function to compute probability of roll of x
double prob(int d, int x)
{
    double p = 0.0, q = 1.0 / dice[d];
    for (int i = 1; i <= dice[d]; ++i)
        if (x - i >= 0)
            p += q * ((P[d-1][x-i] == sentry) ? prob(d-1, x-i) : P[d-1][x-i]);
    P[d][x] = p;
    return p;
}

// program entry point
int main()
{
    int d;
    while (cin >> d)
    {
        if (d == 0) break;
        
        // read the dice
        char j;
        int n, maxroll = 0;
        
        for (int i = 1; i <= d; ++i) {
            cin >> j >> n;
            dice[i] = n;
            maxroll += n;
        }
        
        // read x, the target value
        int x;
        cin >> x;
        
        // check trivial case
        if (x < d || x > maxroll)
            cout << fixed << setprecision(digits) << 0.0 << endl;
        else
        {
            // clear memoization table
            for (int i = 0; i <= d; ++i)
                for (int j = 0; j <= maxroll; ++j)
                    P[i][j] = i ? sentry : 0.0;
            P[0][0] = 1.0;
                    
            cout << fixed << setprecision(digits) << prob(d, x) << endl;
        }
    }
    
    return 0;
}