Let's say we have a group of 1000 animals:
900 rabbits and 100 foxes.
We also know that there are about 10 crimes happening every year and for every crime there's 50% chance of it being committed by a fox.
Then according to Bayes' formula:
P(fox is a criminal) = P(criminal is a fox) * P(animal is a criminal) / P(animal is a fox) = 0.5 * 0.01/0.1 = 0.05 = 5% chance for every given fox to be a criminal.
For every given rabbit the same formula gives 0.5 * 0.01/0.9 which is roughly 0.6%.
Let's say we have a group of 1000 animals: 900 rabbits and 100 foxes.
We also know that there are about 10 crimes happening every year and for every crime there's 50% chance of it being committed by a fox.
Then according to Bayes' formula:
P(fox is a criminal) = P(criminal is a fox) * P(animal is a criminal) / P(animal is a fox) = 0.5 * 0.01/0.1 = 0.05 = 5% chance for every given fox to be a criminal.
For every given rabbit the same formula gives 0.5 * 0.01/0.9 which is roughly 0.6%.