According to official sources, the world’s 7 billionth person was born today. This is a fiction. The goal is to raise awareness about the world’s population. It’s working – the news seems to be all over the blogosphere.
Part of the reason for the fiction is that we don’t have good enough information about populations to be sure what exact day – or even year – the world’s population will pass 7 billion. Counting people, even in developed countries or totalitarian regimes – is tricky.
Another reason is that there may not be a unique 7 billionth person. After all, the population is not increasing steadily. It increases by 1 every time someone’s born, and jumps back down every time someone dies.
On average, there’s
- 4.40 births every second, that is, one birth every 0.227 seconds,
- 1.84 deaths every second, or one every 0.543 seconds, that is,
- The population of the world changes 6.24 times every second. Each time it changes, the chance that it went up is about 7 in 10, and the chance it went down is 3 in 10.
Imagine that in the instant just passed, the 7 billionth child was born. The only way he or she could be the unique 7 billionth child (instead of just one of the several) is if
- the next population change was a birth (only a 7 in 10 chance)
- the one after that is also a birth (another 7 in 10 chance)
- beyond that, there are never enough deaths to outweigh the births and bring the population back to 7 billion.
The chance of just the first two conditions happening is only 7/10 x 7/10, or just under 50%. The exact probability that there’s be only 1 unique 7 billionth child can be worked out with a bit of complicated algebra, using the theory of what are called “Markov Chains”. The chance that there will be only one 7 billionth child is in fact about 3 in 7, or 43%. There’s a 57% chance that there’ll be more than one.
If more than one, then how many?
This is, fortunately, a bit easier to work out. We don’t need Markov Chains any more. Just imagine that the 7 billionth child has just been born. The chance that there’ll be no more 7 billionth children is 43%. However, this is the same, whether or not the child just born is the first, second, fifth or 100th “7 billionth child”.
Therefore,
- The chance that there’s a unique 7 billionth child is 3/7, or 43%.
- The chance that there will be exactly two of them is 4/7 x 3/7 = 12/49, or 24%.
- The chance there will be exactly three of them is 4/7 x 4/7 x 3/7, or 14%.
- The chance that there will be exactly four is 4/7 x 4/7 x 4/7 x 3/7, or 8%.
- The chance that there will be exactly five is 4.6%, and the chance there will be five or more “7 billionth children” is just under 11%.
- The average of all these is that we should expect about 2.33 kids to be able to claim the title of Seven Billionth Human.