easy Probability
A release-checked easy problem for training Law of Total Probability, Coins, Conditional Probability.
Alice and Bob play a game with a coin with probability $0 < p \leq 1$ of heads per flip. Alice starts with the coin and flips it. The game stops when someone flips a heads. If either player flip a tails, they pass the coin to the other player for their turn. However, Bob receives two flips on his turns, while Alice only receives one. Find the value of $p$ such that Alice and Bob are equally likely to win. Round to the nearest thousandth.
This Probability problem is tagged Law of Total Probability, Coins, 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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