RAZD writes:
5· The probability of winning a lottery by any one ticket is extremely low, but the probability that the lottery will be won is extremely high. How do you reconcile these two very disparate probabilities? By knowing that any one of the millions of tickets is a valid winner if picked. To show that this is not the case for the calculations mentioned (ie -- in order to say "1 out of") you have to show that no other combination works of all the other probabilities. There are several different known forms of hemoglobin, all of which do the job of transporting oxygen in the blood, and thus the probability is high that there are other versions that will work as well. Scientists have also manipulated an organism successfully to make it produce an unnatural amino acid, one that does not occur naturally, thus demonstrating that there are other "solutions" than the ones that happen to be used in life as we know it. It could well be that 1 in a million "solutions" of the possible combinations would work, and that the probability would then reduce to 1 in 106. This calculation has not been done and is not included, unnecessarily excluding possible solutions from the probability calculation.
6· Finally, the improbability of a thing occurring is not proof of impossibility of it occurring. It could well be that this is the only planet in all the universe that has life on it because it is a very improbably event. And if you divide the surface of the planet into all the different types of environments and do the same for all the other planets and moons and asteroids in the solar system alone you will have billionsXbillions of little experimental crucibles for carrying out experiments and if that is carried out over several billion year periods (4.55 billion year old earth, in a 13.7+ billion year old universe) with multiple "experiments" in a {day?hour?minute?} ... billionsXbillions of time periods, and do the same for all the billionsXbillions of stellar systems throughout the universe it does not take long to create an equally mind boggling number that reduces improbability down towards a definite probability. I'm at 1054 possiblities already on this one aspect alone ... and for a 1 in 106 chance that looks pretty good.
My maths is pretty ropey, but am I right in thinking if something has 1 chance in
x of occurring, it can never have less than a 63% cumulative chance of occurring at
least once in
x events?
I believe the formula to be:
P = 1-((1-(1/x))^x)
As the number of events increases, so do the probabilities of at least one positive outcome:
2x events = 86%3x events = 95%
. possibly.