11.4. Nyusha has 2022 coins, and Barash has 2023. Nyusha and Barash toss all their coins simultaneously and count how many heads each of them gets. The one who gets more heads wins, and in case of a tie, Nyusha wins. $C$ What is the probability that Nyusha wins?
Solution. Let's assume Barash has temporarily forgotten about his last coin. If Barash has more, he has already won; if Nyusha has more, he has already lost. The chances of these scenarios are equal since they have the same number of coins. If a tie occurs, the forgotten coin will decide the outcome, with each having a 50:50 chance. Therefore, their chances are equal, and the probability of Nyusha winning is 0.5.

Answer. 0.5.