Catching a bus

Here’s why I say math plays an essential role in everything we do.

Bits of DNA

A few years ago Mike Steel wrote a wonderful whimsical short story „My friend and I catch a bus„. It describes a conversation between the narrator (a biologist?) and a friend (a probabilist?) as they take a bus to the movies.

Along the way the narrator learns some statistics: Bayes rule, expectation (of the exponential distribution) and the Poisson distribution. The latter comes up in response to a question about the probability that we are alone in the universe.

The „solution” is as follows: suppose that the probability that life evolves on any given planet is some tiny number p, and that there are a huge number N of planets in the universe. The probability that life evolved on k planets is then approximately

$latex e^{-NP}frac{(NP)^k}{k!}$.

based on the Poisson approximation to the binomial distribution. The question of interest is equivalent to asking for the probability…

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