The probability to pick a spade and then a heart.

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From a standard deck of playing cards, you pick a card and without returning the card you pick a second card. What is the probability that you picked a spade and then a heart?

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There are 4 suits and each suit has 13 cards. In your first draw, you will get a spade with probability 1/4 (each suit is equally likely). Now that you have a spade, there are 51 cards (12 spades and 13 each of the other 3 suits). Now your probability of getting a heart is 13/51. So the probability of getting a spade followed by a heart is $1/4 \times 13/51$.