Suppose \(x \sim B I(n, p)\) follows a binomial distribution of size \(n\) and probability \(p\). Let \(k\) be an integer between 0 and \(n\). Show that \(\operatorname{Pr}(x \geq k)\), looking as a function of \(p\) with \(n\) and \(k\) fixed, is an increasing function of \(p\).