medium Probability
A release-checked medium problem for training Conditional Probability.
A frog starting at position $0$ is going to jump on the integers. At each step, the frog will choose to jump forward $1$ or $2$ steps with equal probability. Let $p_k$ be the probability that the frog hits position $k > 0$. Find the largest value of $p_k$.
This Probability problem is tagged Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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