Tessellate S.T.E.M.S - Mathematics - College - Set 3 - Problem 5

A frog is sitting on the number line at the point $6$ .

Every second, the frog jumps $1$ unit to the left of its position with probability $\dfrac{2}{3}$ or to the right with probability $\dfrac{1}{3}$ .

There's a snake sitting at the point $0$ and a raccoon at $11$ . If the frog jumps on any of them, it is eaten. It isn't difficult to prove that the frog must eventually get eaten.

The probability that the frog is eaten by the raccoon and not the snake, can be expressed as $\dfrac{A}{B}$ ,

where $A,B \in \mathbb{N}$ and $\gcd(A,B)=1$ .

What is $A+B\space ?$

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Hint - Try solving the Gambler's Ruin problem.

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This problem is a part of Tessellate S.T.E.M.S.