Question
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.
To calculate the probability of drawing two diamond cards, we first determine the total number of ways to choose 2 cards out of 52, and then the number of ways to choose 2 diamond cards out of the 13 diamond cards.
Total ways to choose 2 out of 52 cards = 52C2 = (52*51)/(2*1) = 1326
Number of ways to choose 2 diamond cards out of 13 = 13C2 = (13*12)/(2*1) = 78
Therefore, the probability of drawing two diamond cards = 78/1326 ≈ 0.0588
To express the answer in percent form, we multiply by 100 and round to the nearest hundredth:
Probability ≈ 0.0588 * 100 ≈ 5.88%
Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is 5.88%.