To find the probability of drawing either a king or a red card from a standard deck of 52 playing cards, we can use the principle of inclusion-exclusion.
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Count the total number of kings: There are 4 kings in the deck.
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Count the total number of red cards: There are 26 red cards (13 hearts and 13 diamonds).
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Count the overlap: The red cards contain 2 kings (the king of hearts and the king of diamonds). So, we must subtract these 2 from our total when using inclusion-exclusion.
Using the formula for inclusion-exclusion: \[ P(K \cup R) = P(K) + P(R) - P(K \cap R) \]
Where:
- \( P(K) = \frac{4}{52} \) (Probability of drawing a king)
- \( P(R) = \frac{26}{52} \) (Probability of drawing a red card)
- \( P(K \cap R) = \frac{2}{52} \) (Probability of drawing a red king)
Now substituting these values: \[ P(K \cup R) = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} \] \[ = \frac{4 + 26 - 2}{52} = \frac{28}{52} \]
Next, we can simplify this fraction: \[ \frac{28}{52} = \frac{7}{13} \]
Thus, the probability that the card drawn is a king or a red card is \( \frac{7}{13} \).
The correct response is: \( \frac{7}{13} \).