From a well shuffled pack of 52 cards, one card is drawn at random. What is the probability that it is a number card ?

Options

A. `(10)/(13)`
B. `(11)/(13)`
C. `(9)/(13)`
D. `(12)/(13)`

Answer

To find the probability of drawing a number card from a well-shuffled pack of 52 cards, we can follow these steps:

### Step 1: Identify the total number of cards
A standard deck of cards contains 52 cards.

### Step 2: Identify the number cards
In a deck of cards, the number cards are the cards numbered from 2 to 10. Each suit (hearts, diamonds, clubs, and spades) has one of each of these number cards.

- The number cards are: 2, 3, 4, 5, 6, 7, 8, 9, and 10.
- There are 9 number cards in each suit.

### Step 3: Calculate the total number of number cards
Since there are 4 suits, the total number of number cards is:
\[ 9 \text{ (number cards per suit)} \times 4 \text{ (suits)} = 36 \text{ number cards} \]

### Step 4: Calculate the probability
The probability \( P \) of drawing a number card is given by the formula:
\[ P(\text{number card}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes is the number of number cards (36), and the total number of outcomes is the total number of cards (52).

So, the probability is:
\[ P(\text{number card}) = \frac{36}{52} \]

### Step 5: Simplify the fraction
To simplify \( \frac{36}{52} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ P(\text{number card}) = \frac{36 \div 4}{52 \div 4} = \frac{9}{13} \]

### Final Answer
The probability that the card drawn is a number card is \( \frac{9}{13} \).

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