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.
There are 13 diamonds in the deck out of a total of 52 cards, so the probability of drawing a diamond on the first draw is 13/52. Since we do not replace the card, there are now 12 diamonds left out of 51 cards. Therefore, the probability of drawing a second diamond card is 12/51. To find the probability of both events occurring (drawing two diamond cards), we multiply the probabilities:
(13/52) x (12/51) = 3/52
To express this as a percentage, we can divide 3 by 52 and then multiply by 100:
(3/52) x 100 = 5.77%
Rounded to the nearest hundredth, the probability of drawing two diamond cards is approximately 5.77%.