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)
%
The probability of drawing two diamond cards can be calculated as follows:
First, there are a total of 52 cards in a standard deck, so the probability of drawing a diamond card on the first draw is 13/52 = 1/4.
After the first diamond card is drawn, there are now 51 cards remaining in the deck, and 12 of those are diamond cards. Therefore, the probability of drawing a second diamond card is 12/51.
To find the overall probability of drawing two diamond cards, we multiply the probability of the first draw by the probability of the second draw:
(1/4) * (12/51) = 3/51 = 1/17 ≈ 0.0588
To express this probability in percent form, we multiply by 100:
0.0588 * 100 ≈ 5.88%
Therefore, the probability of drawing two diamond cards is approximately 5.88%.