easy Probability
A release-checked easy problem for training Law of Total Probability, Dice, Conditional Probability.
Amber and Billy each have a fair n-sided die, where $n \geq 2$. If Amber rolls a strictly larger value than Billy, she wins. If Amber and Billy roll equal values, Billy wins. Otherwise, both of them roll their die again. The game continues until there is a winner declared. Find the probability that Amber is the winner when $n = 10$.
This Probability problem is tagged Law of Total Probability, Dice, 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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