The king, queen and jack of diamond are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. What is the probability that the card is:
(i) 10 of heart? (ii) a diamond? (iii) a face card?

Answer

To solve the problem step by step, let's analyze each part of the question regarding the probability of drawing specific cards from a modified deck of playing cards.

### Given:
- A standard deck has 52 cards.
- The king, queen, and jack of diamonds are removed.
- Remaining cards = 52 - 3 = 49 cards.

### (i) Probability of drawing the 10 of hearts:

1. **Identify the favorable outcome**:
- There is only 1 card that is the 10 of hearts.

2. **Total outcomes**:
- After the removal of the three cards, the total number of cards left is 49.

3. **Calculate the probability**:
\[ P(\text{10 of hearts}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{49} \]

### (ii) Probability of drawing a diamond:

1. **Identify the favorable outcomes**:
- Originally, there are 13 diamonds in a deck.
- After removing the king, queen, and jack of diamonds, the remaining diamonds = 13 - 3 = 10.

2. **Total outcomes**:
- The total number of cards left is still 49.

3. **Calculate the probability**:
\[ P(\text{diamond}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{10}{49} \]

### (iii) Probability of drawing a face card:

1. **Identify the favorable outcomes**:
- Face cards include the king, queen, and jack from each suit (hearts, diamonds, spades, clubs).
- There are originally 12 face cards (3 from each of the 4 suits).
- After removing the king, queen, and jack of diamonds, the remaining face cards = 12 - 3 = 9.

2. **Total outcomes**:
- The total number of cards left is still 49.

3. **Calculate the probability**:
\[ P(\text{face card}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{9}{49} \]

### Final Answers:
- (i) Probability of drawing the 10 of hearts = \(\frac{1}{49}\)
- (ii) Probability of drawing a diamond = \(\frac{10}{49}\)
- (iii) Probability of drawing a face card = \(\frac{9}{49}\)

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