easy Probability
A release-checked easy problem for training Law of Total Probability, Conditional Probability.
You and a high-stakes friend want to play Russian Roulette together. A revolver with $6$ chambers is loaded with one bullet. Initially, the cylinder is spun to randomize the order of the chambers. The two of you take turns pulling the trigger until the person who fires the gun loses. Given that the cylinder is re-spun after each turn, what is the probability that you win if your friend goes first?
This Probability problem is tagged Law of Total Probability, 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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