If two dice are thrown find probability of getting an odd number one and multiple of 3 on other is

Options

A. `1//3`
B. `1//4`
C. `11//36`
D. `13/36`

Answer

To find the probability of getting an odd number on one die and a multiple of 3 on the other die when two dice are thrown, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When two dice are thrown, each die has 6 faces. Therefore, the total number of outcomes when throwing two dice is:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

2. **Identify the Favorable Outcomes**:
We need to find the outcomes where one die shows an odd number and the other die shows a multiple of 3.

- **Odd Numbers on a Die**: The odd numbers on a die are 1, 3, and 5.
- **Multiples of 3 on a Die**: The multiples of 3 on a die are 3 and 6.

3. **List the Favorable Combinations**:
We will consider cases based on which die shows the odd number and which shows the multiple of 3.

- **Case 1**: Odd number on the first die, multiple of 3 on the second die.
- If the first die is 1: The second die can be 3 or 6 → Outcomes: (1, 3), (1, 6)
- If the first die is 3: The second die can be 3 or 6 → Outcomes: (3, 3), (3, 6)
- If the first die is 5: The second die can be 3 or 6 → Outcomes: (5, 3), (5, 6)

- **Case 2**: Multiple of 3 on the first die, odd number on the second die.
- If the first die is 3: The second die can be 1, 3, or 5 → Outcomes: (3, 1), (3, 3), (3, 5)
- If the first die is 6: The second die can be 1, 3, or 5 → Outcomes: (6, 1), (6, 3), (6, 5)

4. **Count the Favorable Outcomes**:
Now, we will count the total number of favorable outcomes:
- From Case 1: (1, 3), (1, 6), (3, 3), (3, 6), (5, 3), (5, 6) → 6 outcomes
- From Case 2: (3, 1), (3, 3), (3, 5), (6, 1), (6, 3), (6, 5) → 6 outcomes
- Total favorable outcomes = 6 + 6 = 12

5. **Calculate the Probability**:
The probability \( P \) of the event is given by the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{12}{36} = \frac{1}{3} \]

### Final Answer:
The probability of getting an odd number on one die and a multiple of 3 on the other die is:
\[ \frac{1}{3} \]