A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards.

Express your answer in percent form rounding to the nearest hundredth.

1 answer

First, calculate the total number of ways to draw two cards from a standard deck of 52 cards without replacement. This can be done using the combination formula:

52 choose 2 = 52! / (2!(52-2)!) = 1326

Next, calculate the total number of ways to draw two diamond cards from the 13 diamond cards in the deck:

13 choose 2 = 13! / (2!(13-2)!) = 78

Now, calculate the probability of drawing two diamond cards by dividing the number of ways to draw two diamond cards by the total number of ways to draw two cards:

78 / 1326 ≈ 0.0588

Convert the probability to percent form by multiplying by 100:

0.0588 * 100 = 5.88%

Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is approximately 5.88%.