Hi All,
I appreciate all the replies, but I am not sure my question has been answered. DJBruce posted "My entire point was that even with the fact that P(A) is incredibly small, with a large enough number of trials it will happen." May I take this as a "yes" the probability in this case is "1"" answer. I have quite a bit riding on this being true. Can anyone be more specific? What follows is my take on the subject!
The probability that life would occur somewhere in the universe being "1" is a problem which I have not yet resolved to anyone's satisfaction. The idea occurred to me as I was watching Steven Hawkins on a PBS special and he said that given enough time the probability of Earth being struck by something from outer space was "1". To my way of thinking there are many more chances for life to erupt from inanimate elements than there are things in the space surrounding our Sun. We are not talking infinities; we are talking finite numbers. For instance the number of elements which must come together in the right sequence and in the right proportions is about 12. Although modern life is composed of 26 elements, it has been postulated that a primitive life form could probably get by with 12 elements, and possible only 6. I do not know where I got that information, probably out of Science News or one of the other science magazines I used to read. At one time I had two boxes full of articles for my book but a fire got them.
If we consider the case of 12 elements then the number of combinations need to test all combinations is 12 factorial or 479,001,600. If we give the proportions a range of 100 to 1, then we have a possible combination count of 12! X 100! which is in the range of 10^31. Howsoever, if we examine the possible experiments that can be conducted in a universe like ours, and the experiment needs to work only once, we are looking at a much larger number. I have considered one micro liter of water to be sufficient to mix and combine all of the elements required to produce a single living cell. The oceans of Earth are saturated with all 92 elements and they are always moving, joshing the contents around continually. If we allow 1 second per experiment we have 1440 experiments a day times 1.347 x 10^27 (number of micro liters of water on Earth) we get 1.939 x 19^30 experiments per day on planet Earth. In one year we get 7.077 x 10^35. Now if we consider only 1 star in 1000 has liquid water, then we have 7 x 10^19 planets which could possibly produce life. We now have 49.077 x 10^54 experiments per year in the universe. Even if only 1 out of 1000 experiments provided a unique sequence and even if we take a full liter of water for each experiment, we still have 49.077 x 10^45 experiments which is 14 orders of magnitude greater than the number of all the possible combinations of 12 elements in a proportion range of 1 to 100.
If my numbers are anywhere close to accurate then we have many, many more different experiments performed each year that there are possible combinations of 12 elements with a 100 to 1 amount range.
Since all combinations of the necessary elements in a range of proportions must occur somewhere at some time in the universe the probability of life spontaneously forming is "ONE" or inevitable. We humans just won the biggest lottery of them all!
I am sure you will let me know if my numbers are wacky. At age 74 I make a lot of math errors!
