It is a face card, is it a spade?

Question

You draw one card from a standard 52-card deck. A friend peeks and tells you it is a face card (a Jack, Queen, or King). Given that, what is the probability it is a spade?

Accepted Answer

Each of the four suits has exactly three face cards (J, Q, K), so there are 4 	imes 3 = 12 face cards in the deck. The clue restricts you to those 12 equally likely cards. Of them, the spade face cards are the Jack, Queen, and King of spades, which is 3 cards: P(	ext{spade} \mid 	ext{face card}) = \frac{3}{12} = \frac{1}{4}. Because the four suits contribute equally to the face cards, each suit accounts for one quarter of them. Takeaway. Once you know it is a face card, the four suits are symmetric, so the chance of any one suit is simply 1/4.

It is a face card, is it a spade?

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