Probability of drawing a king or a heart

Question

You draw a single card from a well-shuffled standard 52-card deck. What is the probability that it is a king or a heart?

Accepted Answer

Naively adding P(	ext{king}) + P(	ext{heart}) = 	frac{4}{52} + 	frac{13}{52} double-counts one card: the king of hearts. Inclusion-exclusion fixes this: P(K \cup H) = P(K) + P(H) - P(K \cap H) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}. Equivalently, count directly: the 13 hearts plus the 3 non-heart kings make 16 favorable cards out of 52. P = \frac{16}{52} = \frac{4}{13} \approx 0.308. Takeaway. P(A \cup B) = P(A) + P(B) - P(A \cap B). Adding probabilities is only valid for disjoint events, whenever events can overlap, subtract the intersection (and for…

Probability of drawing a king or a heart

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