In a state park, a lost person arrives at a fork with 3 roads: The first road leads back to the same point after 1 hour of walking. The second road leads back to the same point after 2 hours of walking. The third road leads to the parking lot after 5 hours of walking.

There are no signs on the roads and when the lost person arrives back at the fork they have no memory of which road(s) they had taken previously.

5.1 [2 pt] Assuming that the lost person always chooses each road with equal probability, what is the expected amount of time until the tourist arrives at the parking lot?