To find the probability of drawing two diamond cards from a standard deck of 52 cards without replacement, we can follow these steps:
- Total Number of Diamonds: There are 13 diamonds in the deck.
- Total Cards: There are a total of 52 cards in the deck.
Step 1: Probability of the first card being a diamond
The probability of drawing the first diamond is: \[ P(\text{First diamond}) = \frac{\text{Number of diamonds}}{\text{Total number of cards}} = \frac{13}{52} = \frac{1}{4} \]
Step 2: Probability of the second card being a diamond
After drawing the first diamond, there are now 12 diamonds left and only 51 cards remaining in total. The probability of drawing a diamond for the second card is: \[ P(\text{Second diamond | First diamond}) = \frac{\text{Remaining diamonds}}{\text{Remaining total cards}} = \frac{12}{51} \]
Step 3: Joint Probability
To find the probability of both events happening (drawing two diamonds), we multiply the probabilities: \[ P(\text{Two diamonds}) = P(\text{First diamond}) \times P(\text{Second diamond | First diamond}) = \frac{13}{52} \times \frac{12}{51} \] \[ P(\text{Two diamonds}) = \frac{1}{4} \times \frac{12}{51} = \frac{12}{204} = \frac{1}{17} \]
Step 4: Converting to percentage
To express the answer in percent, we convert the fraction to a decimal and then multiply by 100: \[ P(\text{Two diamonds}) \approx \frac{1}{17} \approx 0.058823529 \text{ (approx)} \] Now convert to percent: \[ 0.058823529 \times 100 \approx 5.8823529 \] Rounding to the nearest hundredth gives: \[ 5.88% \]
Final Answer: The probability of drawing two diamond cards is approximately 5.88%.