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.