To determine the probability of selecting a card that is either a club or an ace from a standard deck of 52 cards, we will use the principle of inclusion-exclusion.
- Number of clubs: There are 13 clubs in a standard deck.
- Number of aces: There are 4 aces in the deck, one for each suit.
- Number of aces that are clubs: There is 1 ace that is also a club.
Now, we'll apply the inclusion-exclusion principle to find the total number of favorable outcomes:
\[ \text{Number of clubs} + \text{Number of aces} - \text{Number of clubs that are aces} \]
Plugging in the numbers:
\[ 13 \text{ (clubs)} + 4 \text{ (aces)} - 1 \text{ (ace of clubs)} = 16 \]
Thus, the total number of favorable outcomes (i.e., cards that are either clubs or aces) is 16.
Now, the total number of possible outcomes (total cards in deck) is 52.
The probability \( P \) of selecting a club or an ace is given by the ratio of the number of favorable outcomes to the total outcomes:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{16}{52} \]
Next, we simplify the fraction:
\[ \frac{16}{52} = \frac{4}{13} \quad \text{(by dividing both the numerator and the denominator by 4)} \]
Thus, the probability that the card selected is a club or an ace is
\[ \boxed{\frac{4}{13}}. \]