In a simple card game, Player A wins a point if either a face card, a red prime number, or a black perfect square number is drawn from a standard deck. Otherwise, Player B wins a point. Assume aces do not count as 1s.

Answer 1

- There are 12 face cards (Jack, Queen, King in each suit)
- There are 2 red 5’s (5♥, 5♦)T
- There are 4 Black perfect squares (4♠, 4♣, 9♠, 9♣)

~ There are 18 ways for Player 1 to win.
~ There are 52 – 18 = 34 ways for Player 2 to win.

Therefore, Player 2 has the advantage in this game.

There are a number of ways to make the game fair. For example, Player 1 could win by drawing a 2 or a 7 (in addition to the other possibilities stated earlier.) This will add 8 more chances/cases for Player 1 to win and each player will have 26 ways to win.

Answer 2

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA