How many random walk paths of length 10 reach 5 (or higher), but end at 4 or lower?
I know that the number of paths with $_{10}$ > 4 is equal to the number of paths with $_{10}$ < 4, but I am struggling to incorporate the maximum of $_{10}$ >= 5. I understand that the reflection principle is a key component of this question, but I am having trouble implementing this idea.
How would this question be applied to other problems such as "How many random walk paths of length 10 reach 5 (or higher), and end at 3 or lower?"
I am trying to conceptually understand the idea, so if anyone would be willing to explain, that would be great! Any help would be appreciated. Thanks!