To find the probability of choosing a diamond or a queen in a standard deck of 52 cards, we can calculate it as follows:
- Number of Diamonds: There are 13 diamonds in a deck.
- Number of Queens: There are 4 queens in a deck.
- Overlap: Since one of the queens is a diamond (the queen of diamonds), we need to account for this overlap.
Using the principle of inclusion-exclusion, the probability \( P \) can be calculated as:
\[ P(\text{diamond or queen}) = P(\text{diamond}) + P(\text{queen}) - P(\text{queen of diamonds}) \]
Calculating these probabilities:
- \( P(\text{diamond}) = \frac{13}{52} \)
- \( P(\text{queen}) = \frac{4}{52} \)
- \( P(\text{queen of diamonds}) = \frac{1}{52} \)
Putting it all together:
\[ P(\text{diamond or queen}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13} \]
So the correct approach would be:
\[ \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]
Looking at the options you provided, the one that matches this calculation is:
1352 + 452 - 151
Thus, the probability of choosing a diamond or a queen in a standard deck of cards is best represented by this formula.