private double f(double b) {
    	double PrB=1, p=probLessThan(b);
    	for (int i = 0; i < futureBowls; i++) {
			PrB*=p;
		}
    	double PrA=1-PrB;
    	double ExA=exptGreaterThan(b);
    	double ExB=exptLessThan(b);
    	double Ex2=PrA*ExA+PrB*ExB;
    	return Ex2;
	}