# Stranded Miner

10
Have you seen this question before?

A miner is stranded and there are two paths he can take.

Path $A$ loops back to itself and takes him 5 days to walk it.

Path $B$ brings him to a junction immediately (0 days). The junction at the end of path $B$ has two paths say Path $BA$ and Path $BB$.

Path $BA$ brings him back to his original starting point and takes him 2 days to walk. Path $BB$ brings him to safety and takes him 1 day to walk.

Each path has an equal probability of being chosen and once a wrong path is chosen, he gets disoriented and cannot remember which path he went through, and the probabilities remain the same.

What is the expected value of the amount of days he will spend before he exits the mine?

Next question: Find the missing number
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