A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that it is either red or a king.

Explanation

To solve the problem of finding the probability that a card drawn from a well-shuffled pack of 52 cards is either red or a king, we can follow these steps:

### Step 1: Identify the total number of cards
The total number of cards in a standard deck is 52.

**Hint:** Remember that a standard deck consists of 4 suits, each containing 13 cards.

### Step 2: Count the number of red cards
In a standard deck, there are 2 red suits (hearts and diamonds), and each suit has 13 cards. Therefore, the total number of red cards is:
\[ \text{Number of red cards} = 13 \text{ (hearts)} + 13 \text{ (diamonds)} = 26 \]

**Hint:** Think about how many suits are red and how many cards are in each suit.

### Step 3: Count the number of kings
There are 4 kings in the deck (one from each suit: hearts, diamonds, clubs, and spades).

**Hint:** Recall that each suit has one king.

### Step 4: Count the number of red kings
Among the 4 kings, 2 of them are red (the king of hearts and the king of diamonds).

**Hint:** Identify which suits contain red cards and check how many kings are in those suits.

### Step 5: Apply the principle of inclusion-exclusion
To find the probability of drawing either a red card or a king, we use the formula:
\[ P(\text{Red or King}) = P(\text{Red}) + P(\text{King}) - P(\text{Red and King}) \]

Where:
- \( P(\text{Red}) = \frac{26}{52} \)
- \( P(\text{King}) = \frac{4}{52} \)
- \( P(\text{Red and King}) = \frac{2}{52} \) (since there are 2 red kings)

### Step 6: Substitute the values into the formula
Now, substituting the values we have:
\[ P(\text{Red or King}) = \frac{26}{52} + \frac{4}{52} - \frac{2}{52} \]

### Step 7: Simplify the expression
Combining the fractions:
\[ P(\text{Red or King}) = \frac{26 + 4 - 2}{52} = \frac{28}{52} \]

### Step 8: Reduce the fraction
Now, simplify \( \frac{28}{52} \):
\[ \frac{28}{52} = \frac{7}{13} \]

### Final Answer
Thus, the probability that a card drawn is either red or a king is:
\[ \frac{7}{13} \]

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