Question

a standard deck of 52 cards contains four suits hearts diamonds clubs and spades each suit has 13 cards ace 1 2 3 4 5 6 7 8 9 10 jack queen and king two cars are randomly draw without replacement calculate the probability of drawing two doamand cards express your Nswer in percent from rounding to the nearest hindredth

Answer 1

To calculate the probability of drawing two diamond cards from a standard deck of 52 cards without replacement, follow these steps:

1. **Total number of diamonds in the deck**: There are 13 diamonds in a standard deck.

2. **Probability of drawing the first diamond**:
- The probability of drawing a diamond first is:
\[
P(\text{first diamond}) = \frac{13}{52} = \frac{1}{4} = 0.25
\]

3. **Probability of drawing the second diamond after the first**:
- If the first card drawn is a diamond, there are now 12 diamonds left and a total of 51 cards remaining in the deck.
- The probability of drawing a second diamond is:
\[
P(\text{second diamond} | \text{first diamond}) = \frac{12}{51}
\]

4. **Combined probability of both events**:
- To find the combined probability of both events occurring (drawing two diamonds), multiply the probabilities:
\[
P(\text{two diamonds}) = P(\text{first diamond}) \times P(\text{second diamond} | \text{first diamond}) = \frac{13}{52} \times \frac{12}{51}
\]
- Simplifying this:
\[
P(\text{two diamonds}) = \frac{1}{4} \times \frac{12}{51} = \frac{12}{204} = \frac{1}{17}
\]

5. **Converting to percentage**:
- To convert this probability to a percentage, multiply by 100:
\[
\text{Percentage} = \frac{1}{17} \times 100 \approx 5.8824
\]
- Rounding to the nearest hundredth gives:
\[
\text{Percentage} \approx 5.88\%
\]

Thus, the probability of drawing two diamond cards is approximately **5.88%**.