Question

If you draw three cards from a regular deck of 52 cards, what are the chances they are all hearts?

Answer 1

In a deck of 52 cards, 13 are hearts. Assuming you do not put the cards back in after drawing them, the first card's chance of being hearts would be 13/52, or 1/4. Since on heart card is gone from the deck, the next card's chances of being hearts are 12/51, or 4/17. Now that two hearts are gone from the deck, the third card's chances of being hearts is 11/50. Finally, we have to multiply all three fractions. 1/4 x 4/17 x 11/50 = 44/340, or 11/85. Therefore, our answer is 11/85.

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