You are hiking to a ranger station. There is one correct path. You come to a fork and randomly take the path on the left. You come to another fork and randomly take the path on the right. What is the probability you are still on the correct path?
There is a 1 in 2 chance that you will take the right path at a 2-way fork. However, you went through more than one 2-way forks, so, what you need to do is multiply 1/2 half by itself the number of times you went through a 2-way fork. Since you went through a 2-way fork 2 times, do the following:
(1/2) * (1/2)
You would get the following as your final answer.
There is a 1 in 4 chance that I am still on the correct path.