2 aliens walk on a line meeting probability.

2 aliens walk on a line randomly. At each timestep they walk independently either left or right (1 meter) with equal probability. They start 10 meters apart. What’s the probability that after 7 time steps they have met(Passed though the same point)?


I’m trying to solve this puzzle but I’m struggling. I know that there are $4^7$ states in the tree. If we imagine them being on a number line. Alien A starting at $0$ and Alien B starting at $10$. I know that they can only meet at points 3-7.

I know that the probability of Alien A getting to 3 after 3 time steps is $\frac{1}{8}$.

I don’t really know where to go from here. Thank you for your suggestions.

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