Question 9
Andrew and Bob play with a face-down pile of 2022 cards: 1001 black and the rest white. In each round, two cards are drawn consecutively without replacement. If the first is black and the second white, Andrew wins; if the first is white and the second black, Bob wins. If both have the same colour, play continues to the next round. If Andrew's probability of winning is $x$, find $\lfloor2022x\rfloor$.
Probability model: the face-down deck is randomly shuffled, with all card orderings equally likely.
Probability model: the face-down deck is randomly shuffled, with all card orderings equally likely.