In a standard 52-card deck, there are 4 cards of each rank (one for each suit: hearts, diamonds, clubs, and spades).
To find the probability of selecting either a 4 or a 9, we first count the number of favorable outcomes:
- There are 4 cards that are 4s.
- There are 4 cards that are 9s.
So, the total number of favorable outcomes for selecting a 4 or a 9 is:
\[ 4 , (\text{4s}) + 4 , (\text{9s}) = 8 \]
Now, the total number of possible outcomes when drawing a card from the deck is 52.
The probability \( P \) of selecting a 4 or a 9 is given by the formula:
\[ P(\text{4 or 9}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{8}{52} \]
This can be simplified:
\[ P(\text{4 or 9}) = \frac{2}{13} \]
Therefore, the probability of selecting a 4 or a 9 from a 52-card deck is \( \frac{2}{13} \).