:) 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?

You were on the correct path in the beginning, so it was 100%. You then had a fork of two ways, and taking one randomly leaves you with a 50% chance of being on the right track. The second fork cuts your chances in half again, so 25%. There is a 25% chance you are still on the correct path.