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 find the total number of ways to choose 2 cards out of 52. This can be calculated using the combination formula:
${52 \choose 2} = \frac{52!}{2!(52-2)!} = \frac{52*51}{2} = 1326$
Next, we need to find the number of ways to choose 2 diamond cards out of the 13 diamond cards in the deck. This can be calculated using the combination formula as well:
${13 \choose 2} = \frac{13!}{2!(13-2)!} = \frac{13*12}{2} = 78$
Therefore, the probability of drawing two diamond cards is:
$P(\text{two diamond cards}) = \frac{78}{1326} \approx 0.0587$
Converting this probability to percentage form rounding to the nearest hundredth, we get:
$P(\text{two diamond cards}) \approx 5.87\%$
So, the probability of drawing two diamond cards from a standard deck of 52 cards is approximately 5.87%.