Defective Cat Plushie

A factory produces cat plushies one at a time. Each plushie is either good or defective, and the quality of each plushie depends on the one before it: - If the current plushie is **good**, the next one is also good with probability $\frac{4}{5}$ (and defective with probability $\frac{1}{5}$). - If the current plushie is **defective**, the next one is also defective with probability $\frac{3}{5}$ (and good with probability $\frac{2}{5}$). The factory just produced a defective plushie. What is the expected number of plushies produced until the next defective one (including that next defective plushie)?