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.