To determine the probability of picking a face card from a standard deck of 52 cards, we need to follow these steps:
1. Understand the composition of a deck: A standard deck has 52 cards, divided into 4 suits (hearts, diamonds, clubs, and spades). Each suit contains 13 cards.
2. Identify face cards: In each suit, the face cards are the King, Queen, and Jack, making a total of 3 face cards per suit.
3. Calculate the total number of face cards: Since there are 4 suits and each suit has 3 face cards, we have:
[tex]\[
3 \text{ face cards/suit} \times 4 \text{ suits} = 12 \text{ face cards}
\][/tex]
4. Determine the probability: Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability [tex]\(P\)[/tex] of picking a face card is:
[tex]\[
P(\text{Face Card}) = \frac{\text{Number of face cards}}{\text{Total number of cards}} = \frac{12}{52}
\][/tex]
5. Simplify the fraction: Simplify [tex]\(\frac{12}{52}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{12 \div 4}{52 \div 4} = \frac{3}{13}
\][/tex]
So, the probability of picking a face card from a standard deck of 52 cards is [tex]\(\frac{3}{13}\)[/tex].
Now, let's analyze the given options:
a. [tex]\(\frac{3}{13}\)[/tex]
b. [tex]\(\frac{3}{26}\)[/tex]
c. [tex]\(\frac{14}{52}\)[/tex]
d. [tex]\(\frac{12}{13}\)[/tex]
The correct answer is [tex]\(\frac{3}{13}\)[/tex], which corresponds to option a.
