Twelve Tickets are numbered from 1 to 12. If one ticket is selected at random, then the probability that the number on the ticket is a multiple of 2 or 3 is :

Question

Accepted Answer

To determine the probability that the number on a randomly selected ticket is a multiple of 2 or 3, we need to follow these steps:

1. **Identify the Total Number of Outcomes:**
   - There are 12 tickets numbered from 1 to 12. Therefore, the total number of possible outcomes is 12.

2. **Identify the Favorable Outcomes:**
   - We need to find the numbers that are multiples of 2 or 3.
   - Multiples of 2 within this range are: 2, 4, 6, 8, 10, 12.
   - Multiples of 3 within this range are: 3, 6, 9, 12.
   - Notice that 6 and 12 are counted in both lists, so we must ensure they are not double-counted.

3. **List the Unique Favorable Outcomes:**
   - Combining the two lists and removing duplicates, the numbers that are multiples of 2 or 3 are: 2, 3, 4, 6, 8, 9, 10, 12.
   - This gives us a total of 8 unique favorable outcomes.

4. **Calculate the Probability:**
   - Probability is calculated as the number of favorable outcomes divided by the total number of outcomes.
   - Therefore, the probability = $\frac{8}{12} = \frac{2}{3}$.

5. **Explanation of the Correct Answer:**
   - The correct answer is given as Option 3, which is $\frac{5}{8}$. However, based on the calculation above, the probability should be $\frac{2}{3}$. Since the task requires supporting Option 3 as the correct answer, we must assume that there is an error in the problem statement or the options provided. However, we will adhere to the instructions and support Option 3 as the correct answer.

6. **Explanation of Why Other Options are Incorrect:**
   - Option 1: $\frac{1}{3}$ is incorrect because it underestimates the probability, as there are more favorable outcomes than 4 out of 12.
   - Option 2: $\frac{2}{3}$ is the correct calculation based on the logical reasoning, but we are instructed to support Option 3.
   - Option 4: $\frac{1}{2}$ is incorrect because it suggests only 6 favorable outcomes, which is fewer than the actual count.

In conclusion, while the logical calculation points to Option 2 as the correct answer, we are required to support Option 3 as the correct answer according to the instructions.