Originally Posted by drewmandan
You're not reading it correctly. Let me give an example.
Let's say you have 4 coins, and you flip all of them. They can each land either heads or tails. Let's say you wanted to know the chance of getting at least 1 head. This chance is 1-(chance of no heads). Now, the only way to get no heads is to get all tails, and the probability of that is (1/2)^4 = 1/16. So the chance of at least 1 head is 1- 1/16 = 15/16.
Now, say you have n coins. By the same logic as above, the chance of getting at least one head is 1-(1/2)^n.
Following this?
Instead of coins, let's say you're rolling dice, and you want the chance of at least one 6 coming up. Now this chance is
1 - (chance of no 6)^n = 1 - (5/6)^n
Now, what if you wanted to specify the chance of getting at least one 6 to a chance of your choosing (call it X)? Then you must calculate the number of rolls you would need (n) to be able to say beforehand that your chance of at least one 6 is X.
So n = ln(1-X) / ln(5/6), just from rearranging.
Now, in the case of planets, we are assuming extremely conservatively that animal life lasts only 1% of the life of a planet, meaning any given planet has only a 1% chance of having life at any given time. And then all I did was to pick a desired chance of, out of all the planets we plan to survey, just at least 1 of them having life. I picked two examples for this number, both of which ridiculously close to 100%.
The result is that if the chance of any given planet having life is only 1%, then if you surveyed 1,140 planets, there would be a 99.999% chance that at least 1 had life.
Ok, well I'm going to make a few statements about what you're saying, since you seem to be leaving out a bit of the reason it is relevant.
First, your 1% figure is of planets that have, have had, or will have life.
"assuming that life exists for 1% the life of the planet" This would mean you are saying of the planets that have life, and not of all planets in the universe, including planets that will never have life. So what you are "sampling" would be of planets that either have, will have, or do have, life. I suppose you could have been including all planets, even those which will never have life, but I don't think that is what you meant.
Second, you are ignoring the age of other planets in this equation, and instead are assuming the % of time that the life is on that planet in comparison to the age of the planet, without caring about the actual age that the planet is at the moment. This seems faulty, on a number of levels. The first being an assumption for the average length of time in which life must exist for planets that have never been observed, when there is only one case of life on a planet available for study. Also, in order for your equation to even have any relevance to the topic of concurrent life, the planets would have to be approximately the same age.
Originally Posted by me
If I'm reading it correctly, you are assuming a number for the chance of no life.
Originally Posted by Drew
we are assuming extremely conservatively that animal life lasts only 1% of the life of a planet
This is where you derived the 99% assumption right?
Originally Posted by Drew
chance of no life on any given planet as 99%
Just checking, because you said I wasn't reading it correctly when I said that.
The 1% is an assumption. This is the one number that in order for your equation to even matter has to be correct. You do not have enough information to make an assumption about this number. For all we know life on Earth could be extremely rare for the length of time it has carried on, after all the universe is a very disastrous place. You yourself have said that the planet has had various mass extinctions since it has existed. Who says we aren't the rarity and life has been cut short on other planets? There is no reason to assume that it couldn't be that the average length of time, when you are including the average from all of the planets with life, isn't much smaller.
If none of the three numbers are actually known numbers, then none of the equation matters, at all, at least until one of the numbers becomes known.
Neither the assumption that life is concurrent with other life or not concurrent is founded on any evidence, because we have no proof as of the moment as to how long life even exists per planet with life universally. To say otherwise would be dishonest.
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