A card is drawn at random from a standard $52$-card deck. What is the probability that the card is either a king or a queen?
A$\dfrac{1}{13}$
B$\dfrac{1}{52}$
C$\dfrac{2}{13}$
D$\dfrac{4}{13}$
Answer & Solution
Correct answer: C. $\dfrac{2}{13}$
There are 4 kings and 4 queens in the deck, and no card is both a king and a queen, so these events are mutually exclusive. Using the addition rule:
$P(K \cup Q) = P(K) + P(Q) - P(K \cap Q) = \dfrac{4}{52} + \dfrac{4}{52} - 0 = \dfrac{8}{52} = \dfrac{2}{13}$.
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