The king, queen and jack of diamonds are removed from a pack of 52 playing cards and the pack is well shuffled. A card is drawn from the remaining cards.
Find the probability of getting a card of diamond

Answer

To find the probability of drawing a diamond card after removing the king, queen, and jack of diamonds from a standard deck of 52 playing cards, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Cards:**
A standard deck of playing cards has 52 cards.

2. **Determine the Cards Removed:**
We are removing the king, queen, and jack of diamonds. This means we are removing 3 cards.

3. **Calculate the Remaining Cards:**
After removing these 3 cards, the total number of remaining cards is:
\[ 52 - 3 = 49 \]

4. **Count the Total Diamonds in a Deck:**
In a standard deck, there are 13 diamonds.

5. **Calculate the Remaining Diamonds:**
Since we have removed 3 diamonds (king, queen, and jack), the number of diamonds left in the deck is:
\[ 13 - 3 = 10 \]

6. **Determine the Probability of Drawing a Diamond:**
The probability \( P \) of drawing a diamond is given by the formula:
\[ P(\text{diamond}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Here, the number of favorable outcomes (remaining diamonds) is 10, and the total number of outcomes (remaining cards) is 49. Thus, the probability is:
\[ P(\text{diamond}) = \frac{10}{49} \]

### Final Answer:
The probability of drawing a diamond card is \( \frac{10}{49} \).

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