Question 24
A frog hops along the number line according to the following rules. It starts at $0.$ If it is at $0,$ then it moves to $1$ with probability $\tfrac12$ and it disappears with probability $\tfrac12.$ For $n = 1,$ $2,$ or $3,$ if it is at $n,$ then it moves to $n + 1$ with probability $\tfrac14,$ it moves to $n - 1$ with probability $\tfrac14,$ and it disappears with probability $\tfrac12.$
What is the probability that the frog reaches $4?$
What is the probability that the frog reaches $4?$