But Google already has one successful product, which Yahoo didn't.
It's more like MS. We all remember how badly Bob and those new phones failed. But they went from 0-to-success on the gaming console market, and they did it by capitalizing on their already-successful product ("Hey windows developers, click here to compile your existing game for xbox 360!")
Yahoo! has many successful products. The Yahoo! homepage, Mail, the category leading Answers, News, Sport, and Finance. Those are some of the biggest sites on earth, it seems a bit silly to pretend that Yahoo! doesn't have successful products just because you don't use them.
Yahoo has Yahoo.com, a product that brings in hundreds of millions of users even now. A day or two of placement in the home page is more than enough to launch any product.
I don't know about gmail specifically, but gmail which is part of Google Enterprise solution is "very" profitable as a unit.
You have to look at it this way. All Google's product and services are inter-connected. Unlike tradition software company like MSFT, google doesn't build products for the sole purpose of making profit from start. They make products, and they iterate and years from now if it reaches a tipping point they will start making money off of it. Most of google products are depended on each other's success. So saying things like "Is x product for Google profitable?" is a tricky question.
I am sure they have their separate internal account for each products (or maybe not), but as long as each product drives revenue to its profitable product, but individually not profitable; it makes no difference AFA google is concerned.