The King, Queen, and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is :
(i) a heart (ii) a king

Answer

To solve the problem, we need to determine the probability of drawing a heart and the probability of drawing a king from a modified deck of playing cards.

### Step-by-Step Solution:

1. **Determine the Total Number of Cards Remaining**:
- A standard deck has 52 cards.
- The King, Queen, and Jack of clubs are removed.
- Therefore, the total number of cards remaining is:
\[ 52 - 3 = 49 \]

2. **Calculate the Probability of Drawing a Heart**:
- In a standard deck, there are 13 hearts.
- Since we have not removed any hearts, the number of hearts remains 13.
- The probability \( P(\text{Heart}) \) is given by the formula:
\[ P(\text{Heart}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{13}{49} \]

3. **Calculate the Probability of Drawing a King**:
- In a standard deck, there are 4 kings (one for each suit).
- We have removed the King of clubs, so the number of kings remaining is:
\[ 4 - 1 = 3 \]
- The probability \( P(\text{King}) \) is given by:
\[ P(\text{King}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{49} \]

### Final Answers:
- The probability of drawing a heart is \( \frac{13}{49} \).
- The probability of drawing a king is \( \frac{3}{49} \).