In a game, one card is drawn from a complete deck of playing cards without jokers. If the card is a club or a queen, the gambler wins double his bet. Otherwise, the dealer keeps the money. How much better are the dealer's odds in this game?
A)50% better
B)38% better
C)32% better
D)44% better

Question

Quizplus · Accepted Answer

In a game where the dealer keeps a gambler's wager if he draws any card but a club or queen, his odds are 38% better than the gambler's of winning the money. There are 52 cards in a deck and 13 cards in each suit, including clubs. There are four queens in each deck, but the queen of clubs has already been counted, so only the queens of hearts, diamonds and spades count toward the gambler's list of winning cards. Therefore, the gambler needs one of 16 cards to be pulled in order to win, which make his odds of winning 31%. If his odds are 31%, the gambler's odds are the far superior 69%, which is better by 38%.

In a Game, One Card Is Drawn from a Complete