In one throw of two dice together, find the probability of getting:
(i) a sum of 5
(ii) same number on two dice

Explanation

To solve the problem step by step, let's break it down into two parts as per the question.

### Part (i): Probability of getting a sum of 5

1. **Identify the possible outcomes when rolling two dice**:
Each die has 6 faces, so when rolling two dice, the total number of outcomes is:
\[ 6 \times 6 = 36 \]

2. **List the combinations that give a sum of 5**:
The pairs of numbers that can add up to 5 are:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)

Thus, the favorable outcomes for getting a sum of 5 are:
- (1, 4)
- (4, 1)
- (2, 3)
- (3, 2)

This gives us a total of 4 favorable outcomes.

3. **Calculate the probability**:
The probability \( P \) of getting a sum of 5 is given by the formula:
\[ P(\text{sum of 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{36} = \frac{1}{9} \]

### Part (ii): Probability of getting the same number on both dice

1. **Identify the possible outcomes when rolling two dice**:
As established, the total number of outcomes is still:
\[ 36 \]

2. **List the combinations that give the same number on both dice**:
The pairs that show the same number are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

This gives us a total of 6 favorable outcomes.

3. **Calculate the probability**:
The probability \( P \) of getting the same number on both dice is given by the formula:
\[ P(\text{same number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \]

### Final Answers:
- The probability of getting a sum of 5 is \( \frac{1}{9} \).
- The probability of getting the same number on both dice is \( \frac{1}{6} \).