A release-checked easy problem for training Combinations and Permutations, Coins.
Question
Lewis and Lilly are playing a game with a coin. The coin is going to be tossed $10$ times. After a toss, Lewis will give Lilly $\$1$ if the toss is heads, and Lilly will give Lewis $\$1$ if it is tails. As long as Lewis and Lilly both have at least $\$1$, they will toss again. If one of them has a balance of $\$0$, then the game ends. If they both start out with $\$5$, what is the probability that they break even? That is, what is the probability that both finish the game with $\$5$?
Practice focus
This Probability problem is tagged Combinations and Permutations, Coins. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.