Hi All,
I'm hoping to get some help with a little project I've been pondering for a while. I've been thinking about calculating the chance of life on another planet given that we know it has happened at least once. Essentially what I'm trying to boil this down to is calculating the odds of life occurring on 1 and only 1 planet, versus occurring on at least one planet. Then I can put lower and upper restrictions on what I think the reasonable probability could be then subtract one from the other.
As it has been many years since I was in school a lot of statistics math has left me. So instead of doing the math correctly I 'brute forced' the math by running simulations in excel (crashing excel a few times as I had too many numbers).
So on a galaxy size of 1000 planets I made the probability for each planet 1/1,000,000. Then using the random number generator, generated 1000 planets. Then did this for 702 simulations ('galaxies' if you like). Then I had a probability distribution for the likelihood of having a galaxy with 0, 1, 2, 3 etc planets with life.
I then ran the above multiple times, only changing the probability of life occurring on a planet; 1/100,000, 1/50,000, 1/20,000... to 1/100.
After all that I plotted the likelihood of '1 and only 1 planet' and 'at least one planet' versus the probability of life occurring on each planet. See below.
So my questions are:
What math do I need to plot these without having to set up hundreds of simulations? (I think the word binomial rings a bell) I would like to scale this up to billions of planets and odds of life to 1/billions.
How do I calculate the area under the curve for these graphs. The log scale is throwing me right off, I have no idea where to start.
Also, if anyone has seen someone do something similar that I could read up on, and what glaringly obvious problems have I missed with this idea?
Thanks any and all for your help and input.
I'm hoping to get some help with a little project I've been pondering for a while. I've been thinking about calculating the chance of life on another planet given that we know it has happened at least once. Essentially what I'm trying to boil this down to is calculating the odds of life occurring on 1 and only 1 planet, versus occurring on at least one planet. Then I can put lower and upper restrictions on what I think the reasonable probability could be then subtract one from the other.
As it has been many years since I was in school a lot of statistics math has left me. So instead of doing the math correctly I 'brute forced' the math by running simulations in excel (crashing excel a few times as I had too many numbers).
So on a galaxy size of 1000 planets I made the probability for each planet 1/1,000,000. Then using the random number generator, generated 1000 planets. Then did this for 702 simulations ('galaxies' if you like). Then I had a probability distribution for the likelihood of having a galaxy with 0, 1, 2, 3 etc planets with life.
I then ran the above multiple times, only changing the probability of life occurring on a planet; 1/100,000, 1/50,000, 1/20,000... to 1/100.
After all that I plotted the likelihood of '1 and only 1 planet' and 'at least one planet' versus the probability of life occurring on each planet. See below.
So my questions are:
What math do I need to plot these without having to set up hundreds of simulations? (I think the word binomial rings a bell) I would like to scale this up to billions of planets and odds of life to 1/billions.
How do I calculate the area under the curve for these graphs. The log scale is throwing me right off, I have no idea where to start.
Also, if anyone has seen someone do something similar that I could read up on, and what glaringly obvious problems have I missed with this idea?
Thanks any and all for your help and input.