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Sly Cat
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Probability
Parts
Part 1

You have a pet cat that has a sly tendency to leave your house while you are away. Every day while you are out, you call your neighbor to ask them whether your cat has left your house. Your neighbor always responds with a yes or a no, but sometimes they lie, saying that your cat left when it has not, or vice versa.

Let's say that the probability that your cat leaves the house is 0.001 and the probability that your neighbor lies is 0.1 (independent of whether your cat actually left the house or not).

What is the probability that your cat left the house given that your neighbor says it did so?