Probability and overlapping groups

Multiply probabilities for two events happening together, and subtract the overlap once when adding two groups.

A worked example

Of 60 people, 35 own a bike and 20 own a scooter, with 8 owning both. At least one is 35 + 20 − 8 = 47, so 13 own neither.

The mistake people actually make

Adding the two group percentages counts anyone in both of them twice, so subtract the overlap before taking the total away from 100%.

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