Next We want to determine,for each k,the probability that we hire the best one. And then maximize this probability over all k. Suppose we hire candidate i. i>k in the strategy (since we choose to reject the first k candidates). S:event that we hire the best one. S;:event that we hire the best one,which is candidate i. "Pr[S]=∑=k+1Pr[S]. 11Next ◼ We want to determine, for each 𝑘, the probability that we hire the best one. ◼ And then maximize this probability over all 𝑘. ◼ Suppose we hire candidate 𝑖. ❑ 𝑖 > 𝑘 in the strategy (since we choose to reject the first 𝑘 candidates). ◼ 𝑆: event that we hire the best one. ◼ 𝑆𝑖 : event that we hire the best one, which is candidate 𝑖. ◼ 𝐏𝐫 𝑆 = σ𝑖=𝑘+1 𝑛 𝐏𝐫 𝑆𝑖 . 11