Some other interesting points here: Ballmer works hard to de-emphasize and diplomatically move away from discussing this exact question once it becomes clear that Chang's not approaching it by thinking explicitly about binary search and expected value.

Which is not surprising, because she's a professional journalist! It's amazing that Ballmer (like so many technical interviewers) is so pleased with this question that he couldn't help bringing it up, even though it's not really that relevant to Chang's question.