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 need to determine the total number of ways to draw 2 cards from a deck of 52.
Total number of ways to draw 2 cards from a deck of 52:
= 52C2
= (52 * 51) / (2 * 1)
= 1326
Next, we need to determine the number of ways to draw 2 diamond cards from the deck.
Number of ways to draw 2 diamond cards:
= 13C2
= (13 * 12) / (2 * 1)
= 78
Finally, we calculate the probability by dividing the number of ways to draw 2 diamond cards by the total number of ways to draw 2 cards.
Probability of drawing two diamond cards:
= (Number of ways to draw 2 diamond cards) / (Total number of ways to draw 2 cards)
= 78 / 1326
= 0.0588
Converting this to percent form by multiplying by 100:
= 5.88%
Therefore, the probability of drawing two diamond cards from a standard deck of 52 cards is 5.88%, rounded to the nearest hundredth.