The card is red, is it a heart?

Question

You draw one card from a standard 52-card deck without looking. A friend peeks and tells you the card is red. Given that, what is the probability it is a heart?

Accepted Answer

A deck has two red suits, hearts and diamonds, each with 13 cards, so there are 26 red cards in total. The clue "red" restricts you to those 26 equally likely cards. Of them, 13 are hearts: P(	ext{heart} \mid 	ext{red}) = \frac{13}{26} = \frac{1}{2}. Since the two red suits are the same size, a red card is equally likely to be a heart or a diamond. Takeaway. Conditioning on "red" replaces the full deck with just the red cards; the target's share of that smaller pool is the answer.

The card is red, is it a heart?

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