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:

Total number of cards = 52
Number of cards in each suit = 13
Number of red cards = 26
Number of black cards = 26
Number of queens = 4
Number of kings = 4
Number of aces = 4
Number of face cards = 12

 

Example
A card is drawn from a deck of 52 cards, what is the probability that it is a face card?
 

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

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