Is "heart" independent of "face card"?

Question

You draw a single card from a standard 52-card deck. Consider: - H: the card is a heart. - F: the card is a face card (Jack, Queen, or King). Are H and F independent?

Accepted Answer

Independence requires P(H\cap F) = P(H)\,P(F). - P(H) = 	frac{13}{52} = 	frac14. - P(F) = 	frac{12}{52} = 	frac{3}{13} (three face cards in each of four suits). - P(H\cap F): face cards that are hearts are J, Q, K of hearts, 3 cards, so 	frac{3}{52}. Check the product: P(H)\,P(F) = 	frac14 	imes 	frac{3}{13} = 	frac{3}{52}. It equals P(H\cap F), so H and F are independent. Knowing a card is a heart tells you nothing about whether it is a face card, because face cards are spread evenly across suits. Takeaway. Suit and rank are independent in a standard deck precisely because every ran…

Is "heart" independent of "face card"?

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