In a standard deck of 52 playing cards, there are 4 suits: hearts, spades, diamonds, and clubs. Each suit contains exactly one card numbered 4. Thus, there are a total of 4 cards that are 4s in the entire deck.
To find the theoretical probability of picking a 4 from the deck, we can use the formula for probability:
\[ P(\text{picking a 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
In this scenario:
- The number of favorable outcomes (picking a 4) = 4
- The total number of possible outcomes (total cards) = 52
So, the probability is:
\[ P(\text{picking a 4}) = \frac{4}{52} \]
Next, we simplify the fraction:
\[ \frac{4}{52} = \frac{1}{13} \]
Therefore, the theoretical probability of Lucy picking a 4 from the deck of cards is:
\[ \frac{1}{13} \]