A card is drawn from a pack of 52 cards. Find the probability of getting:
(ii) a king or a diamond

Answer

To solve the problem of finding the probability of drawing either a king or a diamond from a standard deck of 52 cards, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Cards**:
A standard deck contains 52 cards.

2. **Determine the Number of Kings**:
In a deck, there are 4 kings (one from each suit: hearts, diamonds, clubs, and spades).

\[ N(K) = 4 \]

3. **Determine the Number of Diamonds**:
There are 13 diamonds in a deck (one for each rank).

\[ N(D) = 13 \]

4. **Identify the Overlap (King of Diamonds)**:
The king of diamonds is counted in both the total number of kings and the total number of diamonds. Therefore, we need to subtract this overlap to avoid double counting.

\[ N(K \cap D) = 1 \]

5. **Use the Formula for Union of Two Sets**:
The formula for the probability of the union of two events is given by:

\[ N(K \cup D) = N(K) + N(D) - N(K \cap D) \]

Plugging in the values we have:

\[ N(K \cup D) = 4 + 13 - 1 = 16 \]

6. **Calculate the Probability**:
The probability \( P \) of drawing a king or a diamond is given by the ratio of the number of favorable outcomes to the total number of outcomes (the sample space).

\[ P(K \cup D) = \frac{N(K \cup D)}{N(S)} = \frac{16}{52} \]

7. **Simplify the Probability**:
We can simplify \( \frac{16}{52} \) by dividing both the numerator and the denominator by 4.

\[ P(K \cup D) = \frac{16 \div 4}{52 \div 4} = \frac{4}{13} \]

### Final Answer:
The probability of drawing a king or a diamond from a standard deck of 52 cards is:

\[ \frac{4}{13} \]