A card is picked at rnadom from a pack of 52 playing cards. Given that the picked card is a queen , the probability of this card to be a card of hearts is

Options

A. `1/3`
B. `4/13`
C. `1/4`
D. `1/2`

Answer

To solve the problem, we need to find the probability that the card picked is a heart given that it is a queen.

### Step-by-Step Solution:

1. **Understanding the Total Cards**:
- A standard deck has 52 playing cards.

2. **Identifying the Relevant Cards**:
- In a deck, there are 4 queens (one for each suit: hearts, diamonds, clubs, and spades).

3. **Given Condition**:
- We are given that the card picked is a queen. Therefore, we are only considering the 4 queens in the deck.

4. **Favorable Outcomes**:
- Out of the 4 queens, only 1 is a queen of hearts.

5. **Calculating the Probability**:
- The probability of an event is given by the formula:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes (queen of hearts) = 1.
- The total number of outcomes (total queens) = 4.
- Therefore, the probability that the picked queen is a heart is:
\[ P(\text{Heart} | \text{Queen}) = \frac{1}{4} \]

6. **Conclusion**:
- The probability that the card picked is a queen of hearts, given that it is a queen, is \( \frac{1}{4} \).