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To solve the problem of finding the probability that a card is a Queen, given that it is a black card, we can use the concept of conditional probability. 

### Steps:

1. **Identify total number of black cards**:
   In a standard 52-card deck, half of the cards are black (spades and clubs). So, there are \(26\) black cards.

2. **Identify number of black Queens**:
   There are 2 black Queens in the deck (one from spades and one from clubs).

3. **Conditional probability formula**:
   The conditional probability is given by:
   \[
   P(\text{Queen | Black}) = \frac{P(\text{Queen and Black})}{P(\text{Black})}
   \]
   - \(P(\text{Queen and Black})\) is the probability of drawing a black Queen, which is \(\frac{2}{52} = \frac{1}{26}\).
   - \(P(\text{Black})\) is the probability of drawing any black card, which is \(\frac{26}{52} = \frac{1}{2}\).

4. **Calculating the conditional probability**:
   \[
   P(\text{Queen | Black}) = \frac{\frac{1}{26}}{\frac{1}{2}} = \frac{2}{26} = \frac{1}{13}
   \]

5. **Convert to percentage**:
   \[
   \frac{1}{13} \times 100 \approx 7.69\% \approx 8\% \, \text{(rounded to the nearest whole number)}.
   \]

So, the probability that a card is a Queen given that it is a black card is approximately **8%**.

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Would you like more details or have any questions about this? 

Here are 5 related questions to expand your understanding:

1. What is the probability of drawing a Queen from the entire deck?
2. How many red Queens are there in a deck?
3. What is the probability of drawing a face card given that it's red?
4. How does conditional probability differ from regular probability?
5. How can you calculate the probability of drawing an Ace from a black card?

**Tip**: When dealing with conditional probability, always make sure to consider the reduced sample space based on the given condition.

In a well-shuffled, standard 52-card deck, what is the probability that a card is a Queen, given that it is a black card (answer choices are in a percentage format, rounded to the nearest whole number)?

Learn how to solve a conditional probability problem involving a standard 52-card deck. This problem asks for the probability of drawing a Queen, given that the card is black. Suitable for students in Grades 10-12, this problem covers key concepts like conditional probability and basic probability theorems.

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