A card is drawn from a sell shuffled pack of 52 cards. Find the probability of getting:
(i) a red card
(ii) a diamond
(iii) a red card or a jack.

Explanation

To solve the problem of finding the probabilities of drawing certain types of cards from a standard deck of 52 cards, we will break it down into three parts as outlined in the question.

### Step-by-Step Solution:

**(i) Probability of getting a red card:**

1. **Identify the total number of cards:**
- A standard deck has 52 cards.

2. **Count the number of red cards:**
- There are two suits that are red: hearts and diamonds. Each suit has 13 cards.
- Total red cards = 13 (hearts) + 13 (diamonds) = 26 red cards.

3. **Calculate the probability:**
- Probability (P) of drawing a red card = Number of red cards / Total number of cards
- P(red card) = 26 / 52 = 1 / 2.

**(ii) Probability of getting a diamond:**

1. **Identify the total number of cards:**
- A standard deck has 52 cards.

2. **Count the number of diamond cards:**
- There are 13 cards in the diamond suit.

3. **Calculate the probability:**
- Probability (P) of drawing a diamond = Number of diamond cards / Total number of cards
- P(diamond) = 13 / 52 = 1 / 4.

**(iii) Probability of getting a red card or a jack:**

1. **Identify the events:**
- Let event E be drawing a red card.
- Let event F be drawing a jack.

2. **Calculate the probabilities of each event:**
- We already calculated P(E) = 1 / 2 (for red card).
- For jacks, there are 4 jacks in total (one from each suit).
- Probability (P) of drawing a jack = Number of jacks / Total number of cards
- P(jack) = 4 / 52 = 1 / 13.

3. **Identify the overlap (red jack):**
- There are 2 red jacks (jack of hearts and jack of diamonds).
- Probability of drawing a red jack = Number of red jacks / Total number of cards
- P(red jack) = 2 / 52 = 1 / 26.

4. **Use the formula for the probability of either event occurring:**
- P(E or F) = P(E) + P(F) - P(E and F)
- P(red card or jack) = P(red card) + P(jack) - P(red jack)
- P(red card or jack) = (1 / 2) + (1 / 13) - (1 / 26).

5. **Finding a common denominator:**
- The least common multiple of 2, 13, and 26 is 26.
- Convert each fraction:
- (1 / 2) = 13 / 26,
- (1 / 13) = 2 / 26,
- (1 / 26) = 1 / 26.

6. **Combine the fractions:**
- P(red card or jack) = (13 / 26) + (2 / 26) - (1 / 26)
- = (13 + 2 - 1) / 26
- = 14 / 26
- = 7 / 13.

### Final Answers:
- (i) Probability of getting a red card = **1/2**
- (ii) Probability of getting a diamond = **1/4**
- (iii) Probability of getting a red card or a jack = **7/13**