Question

If one card is drawn at random from a well-shuffled deck of 52 playing cards, then the probability of getting a non-face card is

• A. \(\frac{3}{13}\)
• B. \(\frac{10}{13}\)
• C. \(\frac{7}{13}\)
• D. \(\frac{4}{13}\)

Answer 1

The Correct Option is B

Given: A well-shuffled deck of 52 playing cards.

Step 1: Understanding Face and Non-Face Cards 

- A deck has 52 cards. 
- Face cards: Jacks, Queens, and Kings. 
- There are 3 face cards per suit (Hearts, Diamonds, Clubs, Spades). 
- Total face cards = \( 3 \times 4 = 12 \). 
- Non-face cards = \( 52 - 12 = 40 \).

Step 2: Finding the Probability

\[ P(\text{Non-face card}) = \frac{\text{Number of non-face cards}}{\text{Total number of cards}} \] \[ = \frac{40}{52} = \frac{10}{13} \]

Final Answer: \(\frac{10}{13}\)

Answer 2

In a standard deck of 52 playing cards, there are face cards and non-face cards. 
A face card is defined as any card that is a Jack, Queen, or King. Each suit (Hearts, Diamonds, Clubs, Spades) contains 3 face cards: Jack, Queen, King. 
Therefore, there are \(3 \times 4 = 12\) face cards in a deck.

To find the number of non-face cards, subtract the number of face cards from the total number of cards in the deck:
\(52 - 12 = 40\) non-face cards.

The probability of drawing a non-face card is the number of non-face cards divided by the total number of cards:
\(\frac{40}{52}\).

Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
\(\frac{40 \div 4}{52 \div 4} = \frac{10}{13}\).

Therefore, the probability of drawing a non-face card from a well-shuffled deck of 52 playing cards is \(\frac{10}{13}\).