A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a black card nor a king.

Answer

To solve the problem of finding the probability that a card drawn from a pack of 52 playing cards is neither a black card nor a king, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Cards**:
- A standard deck has a total of 52 playing cards.

2. **Determine the Number of Black Cards**:
- There are 2 suits of black cards: Spades and Clubs.
- Each suit has 13 cards, so the total number of black cards is:
\[ 13 \text{ (Spades)} + 13 \text{ (Clubs)} = 26 \text{ black cards} \]

3. **Determine the Number of Kings**:
- There are 4 kings in total (one from each suit: Hearts, Diamonds, Spades, Clubs).

4. **Count the Overlap (Black Kings)**:
- Among the 4 kings, 2 are black (King of Spades and King of Clubs).
- Therefore, when we exclude black cards, we must also exclude these 2 black kings.

5. **Calculate the Total Exclusions**:
- Total cards to exclude:
- Black cards: 26
- Kings: 4
- Black Kings (already counted in black cards): 2
- So, the total number of cards to exclude is:
\[ 26 \text{ (black cards)} + 4 \text{ (kings)} - 2 \text{ (black kings)} = 28 \text{ cards} \]

6. **Calculate the Number of Favorable Outcomes**:
- The number of cards that are neither black nor kings is:
\[ 52 \text{ (total cards)} - 28 \text{ (excluded cards)} = 24 \text{ favorable cards} \]

7. **Calculate the Probability**:
- The probability \( P \) of drawing a card that is neither a black card nor a king is given by the ratio of favorable outcomes to total outcomes:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{24}{52} \]
- Simplifying this fraction:
\[ P = \frac{24 \div 4}{52 \div 4} = \frac{6}{13} \]

### Final Answer:
The probability that the card drawn is neither a black card nor a king is \( \frac{6}{13} \).