A release-checked easy problem for training Conditional Expectation, Markov Chains.
Question
A factory is making cat plushies. Each plushie that gets made can either be of good quality or can be defective. If a cat plushie is of good quality, then the next plushie that gets made is also of good quality with probability $\frac{4}{5}$. If instead a cat plushie is defective, then the next plushie that gets made is also defective with probability $\frac{3}{5}$. If you see that the factory just produced a defective plushie, what is the expected number of plushies that are made before the next defective plushie?
Practice focus
This Probability problem is tagged Conditional Expectation, Markov Chains. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.