Lost Miner and the Maze of Paths

Imagine a miner lost in a maze with two possible paths to choose from: Path A: This path loops back to the beginning and takes 5 days to traverse. Path B: This path leads to a junction instantly (0 days). At the junction, there are two further paths: - Path BA: Leads back to the starting point, taking 2 days. - Path BB: Leads to safety, taking just 1 day. The miner has an equal chance of selecting any path. Once he takes a wrong path, he becomes disoriented and forgets which path he previously took. Calculate the expected number of days the miner will spend in the maze before reaching safety.