A game consists of removing a card from a deck of 52 cards. If the card is a face card, you win $3 and the game is over. If it is not a face card, remove another card. If that one is a face card, you win $3. Repeat the process again, and then again (for a total of 4 times). If you have not removed any face card, then you lose the game, and must pay $3. Should you play this game?
A) no
B) yes

Question

A game consists of removing a card from a deck of 52 cards. If the card is a face card, you win $3 and the game is over. If it is not a face card, remove another card. If that one is a face card, you win $3. Repeat the process again, and then again (for a total of 4 times). If you have not removed any face card, then you lose the game, and must pay $3. Should you play this game? ​
A) no
B) yes

Quizplus · Accepted Answer

The expected value of the game can be calculated to determine if it's beneficial to play. There are 12 face cards (Jacks, Queens, Kings of each suit) and 40 non-face cards in a 52-card deck. The probability of drawing a face card in the first draw is 12/52. If the first card is not a face card, the probability of drawing a face card on the second draw is 12/51, since there are now 51 cards left and still 12 face cards. This pattern continues for the third and fourth draws if necessary. The expected value calculation must consider the probability of winning $3 at each stage and the probability of losing $3 after all four draws without drawing a face card. Given the relatively high probability of drawing a face card within four draws, the expected value is positive, making the game worth playing.

A Game Consists of Removing a Card from a Deck