On Earth, the oldest known fossilized life form is from less than 1 billion years after Earth's formation, and given the difficulty of finding any fossilized life forms before multicellular life, it likely formed long before then. Based on Earth's timeline, abiogenesis actually took much less time than the move to multicellular organisms. While you are correct as far as the statistics go, when given the appropriate conditions, life appears very likely to form within several hundred million years. The cosmos are quite likely rife with microbiology, simply due to the chemicals involved. Any planet with an earth-like chemistry would have all the ingredients for life scattered all over the place. The big question, though, is the likelihood of lifeforms which would be capable of moving towards an intelligent state. The transition from microbiology to macrobiology capable of intelligence in some form or another is a much larger change than a bunch of pre-existing chemicals forming a feedback loop to create more of themselves. Since evolution has no intended end state, if any step along the way to intelligence has a negative cost-benefit, it may make intelligent life much less likely.
@ breadbocks: she is correct; simple cell-membrane base materials are known to form on their own; get enough of together and they form lipid bilayers. These can then form into protocell vesicles capable of letting RNA base pairs pass through, while preventing the longer chains of RNA strands from entering/exiting. On the RNA side of things, the basic ingredients spontaneously form. Thus far, we have found 3 of the 4 RNA base pairs will also then spontaneously form when these ingredients and sunlight meet. Last I remember, the mechanism for creating the fourth using readily available processes on earth is still under investigation. And there you have it. A protocell which is able to gather and contain RNA, absorb more base materials for the protocell vesicle. With relatively widespread formation of these, all that is then required is replication. I can't quite recall the mechanisms for how the early protocells would replicate; aside from a general notion of vesicle division caused by physical conditions in the environment after getting too large and there being some sort of RNA process which will replicate RNA given more base materials.
@pnx: The Sun is classified as G V, a main sequence yellow dwarf, not a subgiant. G class stars, of which our Sun is one, make up 1 in 13 of the stars in the galaxy. They are the third most common, after K and M class stars. Although based on the wiki page for subgiants, both G V (main sequence) and G IV (subgiants) would be capable of hosting habitable worlds
300 billion stars in the galaxy, 23 billion G class, most of which are main sequence (90% of all stars are main sequence), so probably around 10 billion habitation-friendly stars (assuming a good chunk are oddballs which for whatever reason can't support life). If the planet:star ratio is about 1:1 (probably an underestimate of the number of planets), that's 10 billion planets around habitation-friendly stars. Based on Kepler's results (54/1200 planets are in habitable zone), 1 in 22 is in the habitable zone, or 454 million in habitable zones of friendly stars. Since smaller planets are most likely based on the Kepler results, the chance of having a gravity suitable for life is certainly at least 1 in 20 (again, likely a large underestimate), putting it at about 225 million earth-like planets in the habitable zone of a life-friendly star. Even assuming a life-friendly chemical composition is very rare, 1%, a conservative estimate would still put the number of planets upon which life could arise as a million in our galaxy alone. Given there are estimated to be something like 100 billion galaxies in the observable universe, that's hundreds of trillions of planets upon which life could arise.