Small probabilities add up

Rebecca Watson made an excellent video about how the recently-released COVID-19 risk map is not particularly helpful, due to the lack of context provided and the public’s general lack of understanding about how statistics work. It’s well worth watching (and also talks about a few other things, like issues with services like 23andme’s genetic risk factor screening kits). People are apparently using this risk map as a means of justifying going to Thanksgiving gatherings based on “only a 5% infection chance” or the like, which is incredibly short-sighted.

Let’s say that 5% of the population is carrying the disease, and assume that this statistical model is completely accurate. (It almost certainly isn’t, but that’s beside the point.) This means that any time you encounter someone there’s a 5% chance that they’re infected. That seems pretty low, right? For a single encounter, sure. But that doesn’t tell the whole story.

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