# 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**

$P = \dfrac{12}{52} = 0.231$