Question

One card is drawn from a well shuffled deck of 52 cards. Then the probability that the card will be a face card is ________

• A. \( \frac{1}{13} \)
• B. \( \frac{3}{13} \)
• C. \( \frac{5}{13} \)
• D. \( \frac{7}{13} \)

Hint:

When calculating probabilities, remember to count only the specific type of event (like face cards here) in the total possible outcomes.

Answer 1

The Correct Option is B

A standard deck of cards has a total of 52 cards.
So, the total number of possible outcomes is 52.
A face card is a King, Queen, or Jack.
There are 4 suits in a deck: Spades, Hearts, Diamonds, and Clubs.
Each suit has 3 face cards (King, Queen, Jack).
Therefore, the total number of face cards in the deck is $4 \text{ suits} \times 3 \text{ face cards/suit} = 12$.
The number of favorable outcomes (drawing a face card) is 12.
The probability of an event is the ratio of favorable outcomes to the total possible outcomes.
$P(\text{drawing a face card}) = \frac{\text{Number of face cards}}{\text{Total number of cards}}$.
$P(\text{drawing a face card}) = \frac{12}{52}$.
To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which is 4.
$P(\text{drawing a face card}) = \frac{12 \div 4}{52 \div 4} = \frac{3}{13}$.