Let \(I^{s}\) be the current price of a digital option that pays 1 if state \(s\) occurs. \(p^{s}\) is the time 1 value of investing \(I^{s}\) at time \(0, p^{s}=I^{s}(1+r)\), where \(r\) is the one period risk free interest rate. Show that the sum over all states \(s, \sum_{s} p_{s}\), sum to one.