To find the probability of choosing a diamond or a queen from a standard deck of 52 cards, we can use the formula for the probability of either event occurring, which is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Where:
- \( P(A) \) is the probability of drawing a diamond.
- \( P(B) \) is the probability of drawing a queen.
- \( P(A \cap B) \) is the probability of drawing a card that is both a diamond and a queen.
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Probability of drawing a diamond (P(A)): There are 13 diamonds in a deck of 52 cards. \[ P(A) = \frac{13}{52} \]
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Probability of drawing a queen (P(B)): There are 4 queens in the deck. \[ P(B) = \frac{4}{52} \]
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Probability of drawing the queen of diamonds (P(A ∩ B)): There is only 1 queen of diamonds in the deck. \[ P(A \cap B) = \frac{1}{52} \]
Now we can substitute these values into the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] \[ P(A \cup B) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \] \[ P(A \cup B) = \frac{13 + 4 - 1}{52} \] \[ P(A \cup B) = \frac{16}{52} \]
Simplifying that gives: \[ P(A \cup B) = \frac{4}{13} \]
Now, looking at the options given:
- \( \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \) corresponds to our calculation.
Thus, the correct response is: \[ \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]