A standard deck of playing cards contains 52 cards, equally divided among four suits (hearts, diamonds, clubs, and spades). Each suit has the cards 2 through 10, as well as a jack, a queen, a king, and an ace.

If the 3 of spades is drawn from a standard deck and is not replaced, what is the probability that the next card drawn is a spade OR a king?

Question

A standard deck of playing cards contains 52 cards, equally divided among four suits (hearts, diamonds, clubs, and spades). Each suit has the cards 2 through 10, as well as a jack, a queen, a king, and an ace. 

If the 3 of spades is drawn from a standard deck and is not replaced, what is the probability that the next card drawn is a spade OR a king?

anonymous · Answer

In a regular deck, you have 13 spades, and you have four kings. If you take the 3 of spades out, you only have 12 spades, still four kings. One of the kings is a spade, though, and you don't want to count it twice, so you have 12+4-1=15 cards that would satisfy the condition. You have 51 cards in the deck, because you got rid of one of them. So, the probability of drawing a spade or a king is 15/51.

anonymous · Answer

Correct, it just needed to be simplified.

anonymous · Answer

Oh, right, 5/17. Always forget that 51=3*17.