A card is drawn from a pack of 52 cards. Find the probability of getting:
(iv) either a red or a face card.

Answer

To find the probability of drawing either a red card or a face card from a standard deck of 52 cards, we can follow these steps:

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

### Step 2: Count the number of red cards
In a deck, there are 26 red cards (13 hearts and 13 diamonds).

### Step 3: Count the number of face cards
Face cards include Kings, Queens, and Jacks. There are 4 of each type (one for each suit):
- Kings: 4
- Queens: 4
- Jacks: 4

Thus, the total number of face cards is:
\[ 4 + 4 + 4 = 12 \]

### Step 4: Count the number of red face cards
Among the face cards, the red ones are:
- Red Kings: 2 (1 from hearts and 1 from diamonds)
- Red Queens: 2 (1 from hearts and 1 from diamonds)
- Red Jacks: 2 (1 from hearts and 1 from diamonds)

Thus, the total number of red face cards is:
\[ 2 + 2 + 2 = 6 \]

### Step 5: Use the formula for the union of two events
To find the total number of cards that are either red or face cards, we can use the formula for the union of two events:
\[ N(R \cup F) = N(R) + N(F) - N(R \cap F) \]
Where:
- \( N(R) \) = Number of red cards = 26
- \( N(F) \) = Number of face cards = 12
- \( N(R \cap F) \) = Number of red face cards = 6

Substituting the values:
\[ N(R \cup F) = 26 + 12 - 6 = 32 \]

### Step 6: Calculate the probability
The probability of drawing either a red card or a face card is given by:
\[ P(R \cup F) = \frac{N(R \cup F)}{Total \, cards} = \frac{32}{52} \]

### Step 7: Simplify the probability
To simplify \( \frac{32}{52} \):
\[ \frac{32 \div 4}{52 \div 4} = \frac{8}{13} \]

### Final Answer
The probability of drawing either a red card or a face card is:
\[ \frac{8}{13} \]

---