One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting:
(i) a king of red colour.
(ii) a face card.
(iii) a red face card.
(iv) the jack of hearts.
(v) a spade.
(vi) the queen of diamonds.

Answer

To solve the problem, we will find the probabilities for each part step by step.

### Total Cards in a Deck
A standard deck of cards contains 52 cards.

### (i) Probability of getting a king of red colour
1. **Identify the number of favorable outcomes**: There are 2 red kings in a deck (King of Hearts and King of Diamonds).
2. **Calculate the probability**:
\[ P(\text{King of red}) = \frac{\text{Number of red kings}}{\text{Total number of cards}} = \frac{2}{52} = \frac{1}{26} \]

### (ii) Probability of getting a face card
1. **Identify the number of favorable outcomes**: There are 12 face cards in total (3 face cards: Jack, Queen, King from each of the 4 suits).
2. **Calculate the probability**:
\[ P(\text{Face card}) = \frac{12}{52} = \frac{3}{13} \]

### (iii) Probability of getting a red face card
1. **Identify the number of favorable outcomes**: There are 6 red face cards (2 face cards from each of the 2 red suits: Hearts and Diamonds).
2. **Calculate the probability**:
\[ P(\text{Red face card}) = \frac{6}{52} = \frac{3}{26} \]

### (iv) Probability of getting the jack of hearts
1. **Identify the number of favorable outcomes**: There is only 1 Jack of Hearts in the deck.
2. **Calculate the probability**:
\[ P(\text{Jack of Hearts}) = \frac{1}{52} \]

### (v) Probability of getting a spade
1. **Identify the number of favorable outcomes**: There are 13 spades in the deck.
2. **Calculate the probability**:
\[ P(\text{Spade}) = \frac{13}{52} = \frac{1}{4} \]

### (vi) Probability of getting the queen of diamonds
1. **Identify the number of favorable outcomes**: There is only 1 Queen of Diamonds in the deck.
2. **Calculate the probability**:
\[ P(\text{Queen of Diamonds}) = \frac{1}{52} \]

### Summary of Probabilities
- (i) Probability of getting a king of red colour: \(\frac{1}{26}\)
- (ii) Probability of getting a face card: \(\frac{3}{13}\)
- (iii) Probability of getting a red face card: \(\frac{3}{26}\)
- (iv) Probability of getting the jack of hearts: \(\frac{1}{52}\)
- (v) Probability of getting a spade: \(\frac{1}{4}\)
- (vi) Probability of getting the queen of diamonds: \(\frac{1}{52}\)