A card is drawn from a pack of 52 cards. Find the probaility that the card drawn is
(i) a red card (ii) a black card .
(iii) ace of diamonf (iv) a queen or a jack.

Answer

To solve the problem, we need to find the probabilities for four different scenarios when drawing a card from a standard deck of 52 cards.

### Step-by-Step Solution:

1. **Total Outcomes**:
- In a standard deck, there are 52 cards. Therefore, the total number of outcomes when drawing one card is 52.

2. **(i) Probability of Drawing a Red Card**:
- There are 26 red cards in a deck (hearts and diamonds).
- The probability of drawing a red card is calculated as:
\[ P(\text{Red Card}) = \frac{\text{Number of Red Cards}}{\text{Total Number of Cards}} = \frac{26}{52} = \frac{1}{2} \]

3. **(ii) Probability of Drawing a Black Card**:
- Similarly, there are also 26 black cards in a deck (clubs and spades).
- The probability of drawing a black card is:
\[ P(\text{Black Card}) = \frac{\text{Number of Black Cards}}{\text{Total Number of Cards}} = \frac{26}{52} = \frac{1}{2} \]

4. **(iii) Probability of Drawing the Ace of Diamonds**:
- There is only 1 Ace of Diamonds in the deck.
- The probability of drawing the Ace of Diamonds is:
\[ P(\text{Ace of Diamonds}) = \frac{\text{Number of Ace of Diamonds}}{\text{Total Number of Cards}} = \frac{1}{52} \]

5. **(iv) Probability of Drawing a Queen or a Jack**:
- There are 4 Queens and 4 Jacks in the deck, making a total of 8 favorable outcomes.
- The probability of drawing a Queen or a Jack is:
\[ P(\text{Queen or Jack}) = \frac{\text{Number of Queens + Number of Jacks}}{\text{Total Number of Cards}} = \frac{8}{52} = \frac{2}{13} \]

### Final Answers:
- (i) Probability of a red card: \( \frac{1}{2} \)
- (ii) Probability of a black card: \( \frac{1}{2} \)
- (iii) Probability of the Ace of Diamonds: \( \frac{1}{52} \)
- (iv) Probability of a Queen or a Jack: \( \frac{2}{13} \)