Adam the ant starts at (0,0). Each minute, he flips a fair coin. If he flips heads, he moves 1 unit up; if he flips tails, he moves 1 unit right.
Betty the beetle starts at (1,1). Each minute, she flips a fair coin. If she flips heads, she moves 1 unit down; if she flips tails, she moves 1 unit left.
If the two start at the same time, what is the probability that they meet while walking on the grid?
Enter your answer as a fraction in simplest form.