To find the probability of choosing a diamond or a queen from a standard deck of 52 playing cards, we can use the principle of inclusion-exclusion.
- Number of Diamonds: There are 13 diamonds in a deck.
- Number of Queens: There are 4 queens in a deck.
- Number of Queen of Diamonds: There is 1 queen that is also a diamond.
Using inclusion-exclusion, the formula to find the probability \( P(D \cup Q) \) of choosing a diamond (D) or a queen (Q) is:
\[ P(D \cup Q) = P(D) + P(Q) - P(D \cap Q) \]
Where:
- \( P(D) = \frac{13}{52} \) (probability of choosing a diamond)
- \( P(Q) = \frac{4}{52} \) (probability of choosing a queen)
- \( P(D \cap Q) = \frac{1}{52} \) (probability of choosing the queen of diamonds)
Now, substituting these values into the equation gives us:
\[ P(D \cup Q) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \] \[ P(D \cup Q) = \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13} \]
When analyzing your options, we find that the correct formulation aligns with this reasoning:
The response that fits correctly should be:
1352 + 452 - 152
This corresponds to the calculation we performed (\( \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \)).