class jimmy{

public static double r(double k){
    return(0.02+0.01*k);
}

public static double psi(double n,double k){
    if(n == 0)
    	return 1;
    else{
        if (k == 0)
            return 0.1*10*psi(n-1,0)/2/(1+r(k));
        else if (k == n)
            return 0.1*10*psi(n-1,k-1)/2/(1+r(k));
        else
            return 0.1*10*1/2*(psi(n-1,k-1)/(1+r(k-1))+psi(n-1,k)/(1+r(k)));
	}
}

public static void main(String[] args){
 	System.out.println(psi(4,3));
}
}