Question

Problem 3 Suppose a monkey is standing 5 steps from the edge of a cliff. Every second, the monkey either takes one step towards the cliff or one step away from the cliff. He steps towards the cliff with probability $p$ and away with proba- bility $1 - p$. The monkey has no regard for his own life, and continues to do this indefinitely. a) What is the largest value of $p$ for which the monkey will have no more than a 50% chance of eventually falling off the cliff? b) Suppose we have the same situation but with $p = 0.55$. What is the probability that he eventually falls off the cliff? What is the expected length of time for this to happen?

          Problem 3 Suppose a monkey is standing 5 steps from the edge of a cliff.
Every second, the monkey either takes one step towards the cliff or one step away
from the cliff. He steps towards the cliff with probability $p$ and away with proba-
bility $1 - p$. The monkey has no regard for his own life, and continues to do this
indefinitely.
a) What is the largest value of $p$ for which the monkey will have no more
than a 50% chance of eventually falling off the cliff?
b) Suppose we have the same situation but with $p = 0.55$. What is the
probability that he eventually falls off the cliff? What is the expected length of
time for this to happen?

Problem 3 Suppose a monkey is standing 5 steps from the edge of a cliff.
Every second, the monkey either takes one step towards the cliff or one step away
from the cliff. He steps towards the cliff with probability p and away with proba-
bility 1 - p. The monkey has no regard for his own life, and continues to do this
indefinitely.
a) What is the largest value of p for which the monkey will have no more
than a 50% chance of eventually falling off the cliff?
b) Suppose we have the same situation but with p = 0.55. What is the
probability that he eventually falls off the cliff? What is the expected length of
time for this to happen?

Added by Melissa M.

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