Question

Let us play a boy-or-girl-card game. The game contains two cards. One card has one side to be a boy and the other side to be a girl, and the other card has both sides to be the same girl in the first card. Two players play the game. First, one player chooses the girl’s side and the other chooses the boy’s side. On each round, both cards are put into a dark box. Then a third-party person draws a card from the dark box with only one side facing up. If the card has a boy side facing up, turn it over. If the other side is a boy, the person who chose the boy’s side will win this round; otherwise, the person who chose the girl’s side will win this round. However, if the initial card has a girl side facing up, the third-party person will put it back to start over since we already know the other side of this card.

Explain, in terms of probability, that the boy-or-girl-card game is not a fair game.

Who has the advantage and by how much?

Answer 1