6. Edge of Escape I
Setup
A traveler stands in a dark corridor.
Each step, he moves left or right with equal probability.
Rules
- 1 step left: cliff (death)
- 2 steps right: exit (safety)
Question
What is the probability that he survives?
Answer format
Enter a number rounded to 2 decimal places.
Your Answer
Need help?
Hint 1
Let p(x) be the probability of survival starting at position x.
Hint 2
At each position, the traveler moves left or right with equal probability. Write p(x) in terms of p(x-1) and p(x+1).
Hint 3
Use boundary conditions: p(-1) = 0 (cliff) and p(2) = 1 (exit), then solve the system of equations.