To find the probability of choosing a diamond or a queen in a standard deck of cards, we can use the principle of inclusion-exclusion.
- Count the total diamonds: There are 13 diamonds in a deck.
- Count the total queens: There are 4 queens in a deck.
- Count the overlap: There is 1 queen of diamonds.
Using the inclusion-exclusion principle:
\[ P(\text{diamond or queen}) = P(\text{diamond}) + P(\text{queen}) - P(\text{diamond and queen}) \]
Plugging in the values:
\[ P(\text{diamond or queen}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]
Simplifying this gives:
\[ = \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13} \]
Among the given options, the correct expression that captures this probability is:
\[ \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]
So the first option, which is:
\[ \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]
is the correct answer.