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 point)
To calculate the probability of drawing two diamond cards, we first need to find the total number of ways to draw two cards from a standard deck of 52 cards. This can be calculated using combinations:
Total ways to draw 2 cards = 52C2 = 52! / (2! * (52-2)!) = 1326
Next, we need to find the number of ways to draw two diamond cards. Since there are 13 diamond cards in the deck, the number of ways to draw two diamond cards can be calculated using combinations as well:
Ways to draw 2 diamond cards = 13C2 = 13! / (2! * (13-2)!) = 78
Finally, we calculate the probability of drawing two diamond cards by dividing the number of ways to draw two diamond cards by the total ways to draw 2 cards:
Probability = Ways to draw 2 diamond cards / Total ways to draw 2 cards
Probability = 78 / 1326 ≈ 0.0588
Expressing the answer in percentage form:
Probability = 0.0588 * 100% = 5.88%
Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is approximately 5.88%.