To calculate the probability of drawing two diamond cards from a standard deck of 52 cards, we can break it down step by step:
- Total cards in the deck: There are 52 cards in total.
- Total diamond cards: There are 13 diamond cards in the deck.
Probability of drawing the first diamond card: When you draw the first card, there are 13 diamond cards out of 52 total cards. Thus, the probability of drawing a diamond initially is:
\[ P(\text{first diamond}) = \frac{13}{52} \]
Probability of drawing the second diamond card: After drawing one diamond card, there are now 12 diamond cards left and 51 cards remaining in total. Therefore, the probability of drawing a second diamond card after the first is:
\[ P(\text{second diamond | first diamond}) = \frac{12}{51} \]
Calculating the combined probability: To find the overall probability of both events happening (drawing two diamonds in a row), we multiply the two probabilities:
\[ P(\text{two diamonds}) = P(\text{first diamond}) \times P(\text{second diamond | first diamond}) = \frac{13}{52} \times \frac{12}{51} \]
Calculating this gives:
\[ P(\text{two diamonds}) = \frac{13}{52} \times \frac{12}{51} = \frac{13 \times 12}{52 \times 51} = \frac{156}{2652} \]
Now, simplifying \(\frac{156}{2652}\):
\[ \frac{156}{2652} = \frac{1}{17} \quad (\text{since } 156 \div 156 = 1 \text{ and } 2652 \div 156 = 17) \]
Next, we convert this probability into a percentage:
\[ \text{Percentage} = \left(\frac{1}{17}\right) \times 100 \approx 5.88235294117647 \]
Rounding this to the nearest hundredth:
\[ \text{Percentage} \approx 5.88% \]
Therefore, the final answer is:
\[ \boxed{5.88%} \]