Question about statistics

Question

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a spade for the second card drawn, if the first card, drawn without replacement, was a heart? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

13/51 - after a heart is selected, there are 51 cards left, 13 of which are spades.

Answer 2

Card decks are divided evenly into four suits of 15 cards each. If two cards are drawn without replacement and the first is a heart, then after the first draw we have:

15 spades, 15 clubs, 15 diamonds, 14 hearts

for 51 cards left in the deck. We're not replacing our cards, so this is the distribution from which we're pulling our second card. Thus, the probability of pulling a spade is 15/51 or 0.2941.

Answer 3

Hi Mackenzie,

The first draw without replacement yielding a heart means that there are now 51 cards in the deck, 4 of which are spades. Therefore, the probability of getting a spade on the second draw is 4/51.

Hope that makes sense!

-Zach