The Drake equation, here on earth

The Drake equation uses a series of variables to try and estimate the number of possible planets in the galaxy which could send us radio signals:

N = R* * fp * ne * fe * fi * fc * L

Each of these variables is a factor upon which N will depend, like the rate of star formation, and the number of planets that could potentially support life.

Such an approach can be used to estimate a number of quantities. When I became curious about divorce rates and the number of children with divorced parents, I developed one of my own:

CD = CP * MR *(1 – P(D/-C) * (P(D)/P(C)) * FR

I like it both for its mathematical usage and for its collection of random signs and letters that could mean anything until you read the explanation.

CD = Number of children with divorced parents

CP = The population of the country (an obvious starting point)

MR = The marriage rate, generally in the form of marriages per thousand people (e.g. 6.8 per thousand), but here in the form 0.0068

The middle part is based on Bayes’ Theorem, which is a way of working out conditional probabilities, as in, the probability of event A when you know event B happened.

P(D/C) = probability of divorce, given that there is at least one child.

By Bayes’ theorem, P(D/C) = P(C/D)*P(D)/P(C). The only flaw in this is the term P(C/D), which means the probability of a child, given a divorce. However, you can reverse this, so that it’s 1 minus the probability of a divorce, given no children.

P(D) = probability of divorce

P(C) = probability of at least one child (within wedlock).

FR = the fertility rate, the average number of children per family.

Using this equation, the estimated number of children in the US with divorced parents is:

314 million * 0.0068 * (1 – 0.66) * (0.48/0.82) * 1.8 = a little over 750,000 children.

India, with its low divorce rate (the only rates lower than it are in countries where it’s illegal) and high probability of children in a family, has barely 5000 children with divorced parents, in a country with a population four times that of the US. In the UK, there are around 100,000.

However, since this uses the marriage rate, this is divorces per year, meaning that it’s a lot higher. This depends upon the average age of the child(ren) when their parents divorce, which is one statistic I probably won’t find.

Next in the series: how many children have parents who were never married in the first place?

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