One card is drawn from a pack of 52 cards,each of the 52 cards being equally likely to be drawn.Find the probabiltiy if:
(i) the card drawn is red
(ii)the card drawn is a king
(iii) the card drawn is red and a king
(iv) the card drawn is either red or king.

Answer

To solve the problem step by step, we will find the probability for each part of the question.

### Step 1: Probability that the card drawn is red
1. **Total number of cards in a pack**: 52
2. **Number of red cards**: There are 26 red cards (13 hearts and 13 diamonds).
3. **Probability of drawing a red card**:
\[ P(\text{Red}) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{26}{52} = \frac{1}{2} \]

### Step 2: Probability that the card drawn is a king
1. **Total number of kings in a pack**: 4 (one from each suit: hearts, diamonds, clubs, and spades).
2. **Probability of drawing a king**:
\[ P(\text{King}) = \frac{\text{Number of kings}}{\text{Total number of cards}} = \frac{4}{52} = \frac{1}{13} \]

### Step 3: Probability that the card drawn is red and a king
1. **Number of red kings**: There are 2 red kings (king of hearts and king of diamonds).
2. **Probability of drawing a red king**:
\[ P(\text{Red and King}) = \frac{\text{Number of red kings}}{\text{Total number of cards}} = \frac{2}{52} = \frac{1}{26} \]

### Step 4: Probability that the card drawn is either red or a king
1. **Total number of favorable outcomes**:
- Number of red cards = 26
- Number of kings = 4
- Red kings are counted in both categories, so we need to subtract them to avoid double counting.
- Total = Number of red cards + Number of kings - Number of red kings
\[ \text{Total} = 26 + 4 - 2 = 28 \]
2. **Probability of drawing either a red card or a king**:
\[ P(\text{Red or King}) = \frac{\text{Total favorable outcomes}}{\text{Total number of cards}} = \frac{28}{52} = \frac{7}{13} \]

### Summary of Results:
- (i) Probability that the card drawn is red: \(\frac{1}{2}\)
- (ii) Probability that the card drawn is a king: \(\frac{1}{13}\)
- (iii) Probability that the card drawn is red and a king: \(\frac{1}{26}\)
- (iv) Probability that the card drawn is either red or a king: \(\frac{7}{13}\)