The Balance of the Bang: In order for life to be possible in the universe, the explosive power of the Big Bang needed to be extremely closely matched to the amount of mass and balanced with the force of gravity, so that the expansion-speed is very precise. 1 This very exact expansion-speed of the universe, is called the "Cosmological Constant." If the force of the bang was slightly too weak, the expanding matter would have collapsed back in on itself before any planets suitable for life (or stars) had a chance to form, ---but if the bang was slightly too strong, the resultant matter would have been only hydrogen gas that was so diffuse and expanding so fast, that no stars or planets could have formed at all.
Science writer Gregg Easterbrook explains the required explosive power-balance of the Big Bang, saying that, "Researchers have calculated that, if the ratio of matter and energy to the volume of space ...had not been within about one-quadrillionth of one percent of ideal at the moment of the Big Bang, the incipient universe would have collapsed back on itself or suffered runaway relativity effects" (My emphasis.) (ref. G.Easterbrook, "Science Sees the Light", The New Republic, Oct.12, 1998, p.26).
In terms of the expansion rate of the universe as a result of the Big Bang: "What's even more amazing is how delicately balanced that expansion rate must be for life to exist. It cannot differ by more than one part in 10^55 from the actual rate." (My emphasis.) (Ref: H.Ross, 1995, as cited above, p.116). (Note: 10^55 is the number 1 with 55 zeros after it ---and 10^55 is about the number of atoms that make up planet earth).
THE PROBABILITY: The chances we can conservatively assign to this: It was about one chance out of 1021 that the force of the Big Bang could have randomly been properly balanced with the mass & gravity of the universe, in order for stars and planets to form, so that life could exist here in our cosmos.
Leonard Susskind writes in The Cosmic Landscape:
"To make the first 119 decimal places of the vacuum energy zero is most certainly no accident." (The vacuum energy relates to the cosmological constant.) 2
“Logically, it is possible that the laws of physics conspire to create an almost but not quite perfect cancellation [of the energy involved in the quantum fluctuations]. But then it would be an extraordinary coincidence that that level of cancellation—119 powers of ten, after all—just happened by chance to be what is needed to bring about a universe fit for life. How much chance can we buy in scientific explanation? One measure of what is involved can be given in terms of coin flipping: odds of 10^120 to one is like getting heads no fewer than four hundred times in a row. if the existence of life in the universe is completely independent of the big fix mechanism—if it’s just a coincidence—then those are the odds against our being here. That level of flukiness seems too much to swallow.”
Cover America with coins in a column reaching to the moon (380,000 km or 236,000 miles away), then do the same for a billion other continents of the same size. Paint one coin red and put it somewhere in one billion of the piles. Blindfold a friend and ask her to pick the coin. The odds of her picking it are 1 in 10^37
Stephen Hawking writes in A Brief History of Time, p. 125:
"The remarkable fact is that the values of these numbers (i.e. the constants of physics) seem to have been very finely adjusted to make possible the development of life" (p. 125)