Question 1

The probability that the number on the drawn piece of paper will be divisible by 2 but not by 3 is 04-Jan.

In this scenario, the total numbers from 1 to 12 include 6 even numbers: 2, 4, 6, 8, 10, and 12. Among these, the numbers that are divisible by 3 are 6 and 12. Therefore, the numbers that are divisible by 2 but not by 3 are 2, 4, 8, and 10, giving a total of 4 favorable outcomes out of 12 possible outcomes, resulting in a probability of 4/12, which simplifies to 1/3 or 04-Jan.

A) 12-Jan

This option suggests that the probability is 12 out of 12, indicating certainty that any drawn number will meet the criteria. However, not all numbers satisfy the condition of being divisible by 2 but not by 3, making this option incorrect.

B) 04-Jan

This option correctly reflects the probability calculation, as there are 4 favorable outcomes (2, 4, 8, and 10) out of 12 total outcomes. Thus, the probability of drawing a number that is divisible by 2 but not by 3 is indeed 4/12, which reduces to 1/3 or 04-Jan.

C) 03-Jan

This option implies a probability of 3 out of 12, which does not accurately represent the count of numbers divisible by 2 but not by 3. Since there are 4 valid outcomes, this option is incorrect.

D) 12-May

This option incorrectly suggests a probability of 12 out of 5, which is nonsensical in terms of probability representation. It does not correspond to any valid calculation from the context provided, rendering it incorrect.

E) 02-Jan

This option suggests a probability of 2 out of 12, implying that only 2 numbers meet the criteria. However, there are 4 numbers (2, 4, 8, and 10) that satisfy the condition, making this option incorrect.

Conclusion

The correct answer, 04-Jan, accurately represents the probability of drawing a piece of paper with a number divisible by 2 but not by 3, based on the identified valid outcomes. All other options miscalculate or misinterpret the conditions set by the question, confirming that they cannot be correct.