medium Probability
A release-checked medium problem for training Combinatorics, Conditional Probability, Conditional Expectation, Expected Value.
Alice and Bob have fair 30-sided and 20-sided dice, respectively. The goal is to obtain the largest possible value. Alice rolls her die one time. However, Bob can roll his die twice and keep the maximum of the two values. In the event of a tie, Bob is the winner. Find the probability Alice is the winner.
This Probability problem is tagged Combinatorics, Conditional Probability, Conditional Expectation, Expected Value. 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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