Wanna bet? You are giving me 17 billion years and 1 billion correct (i.e., life generating/sustaining/whatever) 96 base-pair-long sequences. Groovy.
Assume that life began in Earth's oceans. The average volume of the ocean is 1.35E18 m^3 or 2.03E27 mm^3. Assume also that, on average, one 96-base pair generating reaction takes place in each cubic millimeter of water each second for 17 billion years. In 17 billion years there will have been 1.09E45 reactions.
Now, there are 4^96 potential 96 base-pair-long sequences. If 1 billion of those are life sustaining, then the chances of a single, random 96 base-pair-long strand being "correct" is 1 in 6.28E48.
From the original article, the "Magic Monkey Formula" for very large numbers approximates (and I quote):
the formula P = 1-(1/(e^R)), where P is the probability of success, R is the ratio of number of trials to number of possible outcomes, and e is a popular mathematical constant having a value of about 2.71828.
R = 1.09E45 / 6.28E48 = 1.74E-4
P = 1-(1/e^1.74E-4) which is roughly equal to 1 in 5759.31.
There are 200 billion stars in the Milky Way. Assume that only 1 in a billion have an Earth-type planet. The odds of life developing in the Milky Way are about 1 in 29.
Now, the Local Cluster of galaxies (of which the Milky Way is part) contains about 30 galaxies. The Milky Way is one of the biggest, so let's say that, on average, there are 50 stars in each galaxy with a planet comparable to Earth. Your odds of life developing in 17 billion years are now better than 1 in 4.
It's past my bedtime and my eyes are starting to cross, so feel free to point out any errors I made in the application of the formula or the calculation thereof. My assumptions, of course, are still up for debate.
96 base pairs is the maximum possible natural limit per the math in this thread, not the minimum number of required base pairs for life. An amoeba will have over 600 Million base pairs for its life in its DNA...