medium Probability
A release-checked medium problem for training Conditional Expectation, Conditional Probability, Markov Chains.
Albert rolls a standard fair 6-sided die with the values $1-6$ on the sides. He continually rolls the die and keeps track of the outcomes in the order they appear. Albert rolls until he sees either $2$ $5$s (not necessarily consecutive) OR both a $4$ and a $6$. Find the probability that Albert stops rolling due to seeing a $4$ and a $6$.
This Probability problem is tagged Conditional Expectation, Conditional Probability, Markov Chains. 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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