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June 25th, 2019, 09:53 PM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Probability of living at a certain time
The human populatio is growing exponentially. An example of the human population could be: Year 1800: population 1.75 billion Year 1900: population 3.5 billion [1.75 * 2] Year 2000: population 6 billion [1.75 * 2 * 2] The question is: Given any person which year is that person more likely to live in? My attempt: P(y) = probability of being born in year y u = number of people that you could've been at any given year t = total number of people So $\displaystyle P(y) = \frac{u}{t}$ n(t) is clearly the population at any given year. The difficulty I have is calculating n(u). May be we don't need to find u at all and a good estimate is possible. I'm not sure. Any help will be deeply appreciated. Thanks 
June 26th, 2019, 08:28 AM  #2 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 650 Thanks: 86 
I'm assuming you made a typo because 1.75 * 2 * 2 is 7, not 6. If your question is as simple as only working with the three years you gave, the probabilities are 1/7 for 1800, 2/7 for 1900, and 4/7 for 2000. If you want generic calculations, would you like to assume exponential growth that doubles every 100 years? In that case, the annual growth is about 0.6956 percent. More specifically, 1.00695555555501^100 = 2.000001081. Life expectancy increases over time. Even if you had the worldwide life expectancy for each year, the amount of time people live for is not normally distributed. If the life expectancy from Year X to Year Y increases 10 percent, you can't conclude that Year Y will have 10 percent more people at Age Q.

June 27th, 2019, 06:48 PM  #3  
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Quote:
Can you show me how you got these numbers? Thanks. Here are my thoughts on the matter: We need to find out: 1. u = number of instances that you could be given any particular year x 2. t = total number of people alive in that given year x t is fairly easy as its the total population given any particular year P(living in year x) = u/t t is fairly easy as its the total population alive in any given year. How do you calculate u?  
June 27th, 2019, 07:00 PM  #4  
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Quote:
In my opinion the P(being alive in year x) = $\displaystyle \frac{u,\text{ number of people you could be in year x}}{t,\text{ the total population of the year x}}$ Calculating t is simple, because it's just the total population given any one year; u is trickier. How do we get a fix on which outcomes would satisfy the condition of being you? Is it as simple as the outcomes that satisfy being you increase with the population. It's said that populations grow exponentially. However, every single person is unique, implying that u = 1 at all times. IF that's the case, then the P(being alive in year x) decreases with time as population is always increasing. However if we look at it from the perspective that u may increase with the population. For instance, if you're an Indian then P(being an Indian in year x) = (number of Indians given a year x)/(total population of the earth). I believe the Indian population is exploding at the moment and so P(being Indian in year x) would also increase if the numbers are in the correct proportion. Last edited by skipjack; June 28th, 2019 at 02:26 AM.  
June 28th, 2019, 05:40 PM  #5 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 650 Thanks: 86 
I think I was answering a different question than you were asking. I was working with the probability that a person would be alive at a certain year given the population of different years. What you want to know is if one person is randomly selected from everybody alive at the time, what is the probability of it being you? The answer is 1 divided by the world's population. To calculate of a random person being from a specific country, having a name that starts with A, being unemployed, or any other group, you need to know how many people are in that group at the time. My 1/7, 2/7, and 4/7 came from: 1.75 billion/(1.75 billion + 3.5 billion + 7 billion) = 1/7 3.5 billion/(1.75 billion + 3.5 billion + 7 billion) = 2/7 7 billion/(1.75 billion + 3.5 billion + 7 billion) = 4/7 

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