Probability Problems Involving Cards
A standard deck has 52 cards with 4 suits, namely, hearts (♥), diamonds (♦), clubs (♣), and spades (♠). Hearts and diamonds are color red while clubs and spades are color black. Cards in each suit contains 3 face cards (jack, queen, and king) and 10 numbered cards. The card numbered as 1 is called ace.
The following are the complete list of standard cards:
| A♥ | A♦ | A♣ | A♠ |
| 2♥ | 2♦ | 2♣ | 2♠ |
| 3♥ | 3♦ | 3♣ | 3♠ |
| 4♥ | 4♦ | 4♣ | 4♠ |
| 5♥ | 5♦ | 5♣ | 5♠ |
| 6♥ | 6♦ | 6♣ | 6♠ |
| 7♥ | 7♦ | 7♣ | 7♠ |
| 8♥ | 8♦ | 8♣ | 8♠ |
| 9♥ | 9♦ | 9♣ | 9♠ |
| 10♥ | 10♦ | 10♣ | 10♠ |
| J♥ | J♦ | J♣ | J♠ |
| Q♥ | Q♦ | Q♣ | Q♠ |
| K♥ | K♦ | K♣ | K♠ |
Some useful details:
|
Number of cards in each suit = 13 Number of red cards = 26 Number of black cards = 26 |
Number of face cards = 12 Number of cards per denomination = 4 Total number of cards = 52 |
Example
A card is drawn from a deck of 52 cards, what is the probability that it is a face card?
Solution
$P = \dfrac{12}{52} = 0.231$