Google Produktmanager interview questions

Phone screened twice as the first position evaporated after a very positive initial phone screen process and I was forced back to square one. In the first screen, I was asked to estimate the number of windows in all of Manhattan, which I answered quite well. The second screener rejected me almost certainly because I wasn't able to adequately solve the probability question below in my head on the spot.

Had a phone interview, which consisted of 3 parts: Strategical - where I was asked about the strategy behind Chrome browser and OS ; Analytical - where I was asked to analyze a new feature for YouTube ; and Techincal - where I was asked about how online authentication works.